Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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graph this line using intercepts: 42x - 60y = -4,200 click to select po…
To graph the line \( 42x - 60y = -4200 \), plot the x-intercept \( (-100, 0) \) and y-intercept \( (0, 70) \), then draw a line through these two points.
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graph this line using intercepts: x - 9y = 9 click to select points on …
To graph the line \( x - 9y = 9 \), plot the x - intercept \( (9, 0) \) and the y - intercept \( (0, -1) \), then draw a straight line through these two points.
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graph this line using intercepts: 7x - y = 7 click to select points on …
The x - intercept is \( (1, 0) \) and the y - intercept is \( (0, - 7) \). The line is graphed by plotting these two points and drawing a line through them.
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graph this line: y + 2 = x + 9 click to select points on the graph.
To graph the line \(y=x + 7\) (derived from \(y + 2=x + 9\)): - Plot the y - intercept at \((0,7)\). - Plot another point, for example, when \(x=-7\), \(y = 0\) (point \((-7,0)\))…
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the two polygons below are similar. complete the similarity statement. …
$EHGF$
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solve the inequality $x + 6 < 10$ $x+6 < 10$ $-6$ $-6$ $x < 4$ subtract…
The solution is $x < 4$. The graph has an open circle at 4 with an arrow extending to the left along the number line.
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graph this line: y + 4 = -5(x + 8) click to select points on the graph.…
To graph the line \( y + 4=-5(x + 8) \), plot the points \( (-8,-4) \) and \( (-9,1) \) (or other points found using the slope - point form or slope - intercept form) and draw a s…
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solve the inequality $y - 8 > -6$. $y - 8 > -6$ $\\underline{\\quad\\qu…
The solved inequality is $\boldsymbol{y > 2}$. For the graph: place an open circle at 2 on the number line, and shade the region to the right of 2. All values greater than 2 are i…
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1 calculate the distance from the point a(-3,2) to the line y = 2x + 1.…
s: 1. \( \boldsymbol{\frac{7\sqrt{5}}{5}} \) 2. \( \boldsymbol{\frac{3\sqrt{2}}{2}} \) 3. \( \boldsymbol{\frac{4}{5}} \) 4. \( \boldsymbol{\sqrt{5}} \) 5. \( \boldsymbol{\frac{6\s…
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1 the cost for an upcoming field trip is $30 per student. the cost of t…
B. 30, D. 90 ### Question 2 The area of a rectangle \( A=l\times w \), given \( A = 24\space cm^{2}\), so the length \( l=\frac{24}{w}\), and the width \( w>0\) (since width of a …
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cyu perimeter and area of composite shapes 1. determine the area and pe…
### Part (a) #### Step 1: Analyze the Composite Shape The shape can be considered as a rectangle formed by combining the given segments. Let's find the length and width. - The hor…
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cyu perimeter and area of composite shapes 1. determine the area and pe…
Perimeter: \(\boldsymbol{48}\) m, Area: \(\boldsymbol{71}\) m² ### Part (b)
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let’s start by looking at angle abc. click the button to display the pr…
\( 80^\circ \)
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lets start by looking at angle abc. click the button to display the pro…
To solve for the measures of the interior angles of triangle \( ABC \) and their sum, we follow these steps: ### Step 1: Measure \( \angle ABC \) Use a protractor to measure \( \a…
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1. what is the value of x? 83 58
58
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answer the following question in the picture. * lesson 8: exit ticket a…
\(\sin(D)=\frac{4}{5}\), \(\cos(D)=\frac{3}{5}\), \(\tan(D)=\frac{4}{3}\)
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use the given information to prove that $\\triangle sqr \\cong \\triang…
The reason for step 3 is "Hypotenuse - Leg (HL) Congruence Theorem (since \(\triangle SQR\) and \(\triangle QSP\) are right triangles, \(\overline{SQ}\cong\overline{SQ}\) (reflexi…
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3x - y = 9 click to select points on the graph.
Plot the points $(3, 0)$, $(0, -9)$, and $(2, -3)$, then draw a straight line through them to graph $3x - y = 9$.
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11. \\begin{cases} y \\leq -\\frac{3}{5}x \\\\ y > -x - 4 \\end{cases}
The solution is the overlapping shaded region: below the solid line $y=-\frac{3}{5}x$ and above the dashed line $y=-x-4$. (On the provided grid, this overlapping area covers point…
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independent practice write and solve an equation to find the measures o…
\(\angle A = 76^\circ\), \(\angle B = 63^\circ\), \(\angle C = 41^\circ\) ### Problem 2:
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6. which angle pairs form complementary angles? diagram with angles at …
The complementary angle pairs are \(\angle ABE\) (25°) and \(\angle EBF\) (65°), and \(\angle DBE\) (50°) and \(\angle FBC\) (40°). (Or in terms of angle labels: \(\angle ABE\) an…
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y - 7 = -\\frac{9}{5}(x + 10) click to select points on the graph. grap…
Plot the points $(-10, 7)$, $(-5, -2)$, and $(0, -11)$, then draw a straight line through them.
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use the given information to prove that $\\triangle def \\cong \\triang…
To prove $\triangle DEF \cong \triangle HGF$, we use the AAS (Angle - Angle - Side) congruence criterion: ### Step 1: Identify Vertical Angles - **Statement**: $\angle DFE \cong \…
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5. $\\angle m$ and $\\angle n$ are supplementary and $m\\angle m = 37^\…
\(37 + 13x = 180\) ### Part b: Solve for \(x\) and \(m\angle N\)
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read the following passage from night. in the passage, elie wiesel and …
C. It highlights Meir Katz’s initial strength so the reader can better understand how dramatically he changes during the journey.
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use the given information to prove that $\\triangle def \\cong \\triang…
1. Reason: Given 2. \(\overline{DF} \cong \boldsymbol{\overline{HF}}\) 3. Reason: Vertical angles are congruent 4. Reason: SAS (Side - Angle - Side) Congruence Criterion
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16. the volume of the rectangular prism below is $36x^6y^8$. determine …
### Question 16 (Volume of Rectangular Prism) # Explanation: ## Step 1: Recall Volume Formula The volume \( V \) of a rectangular prism is given by \( V = l \times w \times h \), …
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problem set 1: properties of real numbers identify the property that ju…
Let's solve each problem by identifying the property of equality or congruence: ### Problem 1 - **Statement**: \( m\angle ABC = m\angle XYZ \) - **Property**: Reflexive Property (…
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triangles independent practice write and solve an equation to find the …
\( \angle A = 76^\circ \), \( \angle B = 63^\circ \), \( \angle C = 41^\circ \) ### Problem 2: Triangle DEF
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use the given information to prove that $\\triangle adb \\cong \\triang…
To prove $\triangle ADB \cong \triangle CDB$: 1. From $\overline{BD} \perp \overline{AC}$, we have $\angle ADB=\angle CDB = 90^{\circ}$ (definition of perpendicular lines). 2. Fro…
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name problem set 1: properties of real numbers > identify the property …
Reflexive Property of Congruence ### Problem 4: $GH \cong MN$ and $MN \cong OP$, so $GH \cong OP$
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use the given information to prove that $\\triangle def \\cong \\triang…
1. Reason for \(\overline{EF} \cong \overline{GF}\): Given 2. \(\angle EDF \cong \angle \boldsymbol{GHF}\) (Given) 3. Reason for \(\angle DFE \cong \angle HFG\): Vertical angles a…
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a number of squares are connected in a row to form a rectangle. the tab…
- The table can be represented by the equation $y = 4x + 4$. - The relation is a function. - The graph of the function is linear.
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what fraction of the entire 6 × 4 grid is covered with colored tiles? h…
\(\frac{2}{3}\)
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fractions simplifying fractions simplify each fraction by using the cor…
$\frac{1}{2}$ (GCF circled: 16) #### b) $\boldsymbol{\frac{27}{30}}$
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additional example 1 find the sum of the interior angles of the polygon…
The sum of the interior angles of the polygon (quadrilateral) is \( 360^{\circ} \)
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graph the system of equations. $y = \\frac{4}{5}x + 1$ $y = -\\frac{1}{…
The system of equations \( y=\frac{4}{5}x + 1 \) and \( y=-\frac{1}{5}x+6 \) intersects at the point \( (5,5) \). To graph the system, plot the y - intercepts \( (0,1) \) for the …
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applying the pythagorean theorem what is the value of x? x = (right tri…
\(x = 6\)
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modeling parallel and perpendicular lines line ql is represented by the…
Slope of Line QL (\(m_1\)): \(1\) Slope of Line GN (\(m_2\)): \(1\) Point - Slope Form of Line GN: \(y - (-2)=1(x - 0)\) (or \(y + 2 = x\)) Equation of Line GN in slope - intercep…
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the diagram shows a regular polygon. what is the value of x? write your…
\( x = 90 \)
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the diagram shows a convex polygon. what is the value of a? a = \\boxed…
\( a = \boxed{71} \)
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what is the measure of an exterior angle in a regular polygon with 13 s…
\( 27.7 \)
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the diagram shows a convex polygon. what is the value of ( v )? ( v = s…
\( v = 69 \)
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what is the measure of an exterior angle in a regular triangle? write y…
\(120\)
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what is the sum of the exterior angle measures, one at each vertex, of …
\( 360 \)
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what is the measure of an exterior angle in a square? write your answer…
\(90\)
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the diagram shows a regular polygon. what is the value of x? write your…
\( 90 \)
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the diagram shows a regular polygon. what is the value of x? write your…
$x = \boxed{120}$
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4) $-10(x + 6) < -170$ 6 7 8 9 10 11 12 13 14 15 16
$x > 11$ (Graph: Open circle at 11, arrow pointing right on the given number line)
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how does the number of sides of a convex polygon, n, relate to the sum …
The sum of the interior angle measures of a convex \(n\)-sided polygon is \(180^{\circ}\cdot(n - 2)\), where \(n\) is the number of sides. As \(n\) increases by 1, the sum increas…
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choose the triangle shortcut that can be used to state the triangles be…
The triangles are not congruent.
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two angles are complementary. the first angle measures 37°. what is the…
$53^\circ$
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what is the surface area? image of a rectangular prism with length 8 cm…
150 square centimeters
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the students in mrs. hollands preschool class sit down in a circle for …
12.57 meters
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choose the triangle shortcut that can be used to state the triangles be…
Side Angle Side
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4. circle the trapezoid made with fewer blocks. 5. ling measures a frog…
4. Circle the right trapezoid (the smaller, narrower dark trapezoid on the right) 5. 5 cm
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a line that includes the points (3, -1) and (w, 6) has an undefined slo…
3
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a line with a slope of $-\frac{5}{4}$ passes through the points $(4, -1…
\( k=-4 \)
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rotating δpqr by 180° clockwise about the origin, we get its image δpqr…
(a) $CP = CP' = \sqrt{74}$ units $CQ = CQ' = \sqrt{45}$ units $CR = CR' = \sqrt{65}$ units (b) $180^\circ$ (c) Each point on the original figure is the same distance from the cent…
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rotating $\triangle lmn$ by $90^circ$ clockwise about the origin, we ge…
(a) $90^\circ$ (b) $CL = CL' = \sqrt{65}$ units $CM = CM' = \sqrt{34}$ units $CN = CN' = 6\sqrt{2}$ units (c) All angles formed by a point and its image, with the vertex at the ce…
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rotating $\\triangle abk$ by $90^\\circ$ counterclockwise about the ori…
### (a) $CA = CA' = \sqrt{37}$ units $CB = CB' = 5\sqrt{2}$ units $CK = CK' = \sqrt{53}$ units ### (b) $m\angle ACA' = m\angle BCB' = m\angle KCK' = 90^\circ$ ### (c) Each point o…
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identify all the obtuse isosceles triangles. obtuse isosceles not obtus…
The obtuse isosceles triangles are the first (left - most) and the sixth (right - most) triangles in the given set (the ones with two equal sides and one obtuse angle).
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use the figure to complete each part. (a) name the sides of ∠tqr. qt an…
s: (a) The sides of $\angle TQR$ are $QT$ and $QR$. (b) Two other names for $\angle 2$ are $\boldsymbol{\angle SQR}$ and $\boldsymbol{\angle RQS}$ (or $\angle Q$ and $\angle SQR$ …
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problem 6 change one of the values to make this triangle a right triang…
| x | y | z | |----|------|------------| | 4 | 6 | $2\sqrt{13}$ | | 4 | $\sqrt{33}$ | 7 |
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(a) name the sides of ∠tqr. (b) write two other names for ∠2. (c) name …
\( QT \), \( QR \) ### Part (b)
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classify the four angles of the quadrilateral. figure of quadrilateral …
- \(\angle A\): Right - \(\angle B\): Acute - \(\angle C\): Obtuse - \(\angle D\): Right (To fill the table: For \(\angle A\) and \(\angle D\), select "Right"; for \(\angle B\), s…
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use the figure to find the value of x. (a) write an equation to find x.…
The equation is \(13x + 10 = 166\) and \(x = 12\).
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b. the table shows the ordered pairs of the points that give the approx…
1. Plotted and labeled points: $H(6,3)$, $I(4,0)$, $J(0,1)$, $K(-2.5,2)$, $L(-4,2.5)$, $M(6,-1.5)$, $N(-3.5,-0.5)$ on a coordinate plane. 2. Connected points in the order $D \to C…
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problem 5 tiam the turtle is traveling on one side of a triangle. exact…
$\sqrt{2}$ units
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points in space 5. for parts (a)-(d), consider the star map that shows …
| Point | Ordered Pair | |-------|--------------| | A | $(3, -3)$ | | B | $(-1, 0)$ | | C | $(-5, 4)$ | | D | $(-7, 4)$ | | E | $(-2, -5)$ | | F | $(0, -2)$ | | G | $(1, 3)$ |
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in the figure below, m∠abd = 112°. (a) write an equation to find x. mak…
\( 3x + 52 = 112 \)
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in the figure below, m∠abd = 112°. (a) write an equation to find x. mak…
\( 3x + 52 = 112 \)
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(a) write an equation to find x. make sure you use an \=\ sign in your …
The correct equation to find \(x\) is \(15x - 37=113\) (and the solution for \(x\) is \(x = 10\) since \(15x=150\) when we add 37 to both sides of the equation \(15x - 37=113\)). …
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problem 4 explain when ( a^2 + b^2 = c^2 ) is true for triangles. use t…
The equation $a^2 + b^2 = c^2$ (the Pythagorean theorem) is true **if and only if the triangle is a right triangle**, where $a$ and $b$ are the lengths of the two legs (the sides …
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solve. you may use a calculator. the swimming pool at lake spring high …
The combined area of the pool and tiled floor is \( \boldsymbol{4x^{3}+138x^{2}+390x + 4225} \) square meters. ### 2. Find the area of the tiled floor.
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use the figure to find the value of x. (a) write an equation to find x.…
The equation is \(15x - 37 = 113\) and the value of \(x\) is \(10\).
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an electric toy train travels around a christmas tree in a circle. the …
The train travels $6\pi$ feet (or approximately 18.84 feet)
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here are pairs of complementary and supplementary angles. describe what…
Complementary angles... are two angles whose measures add up to 90°. Supplementary angles... are two angles whose measures add up to 180°.
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triangles abd and ace are similar right triangles. which best describes…
The correct option is the fourth one (the one with \(\frac{BD}{DA}=\frac{CE}{EA}\) so \(\frac{4}{2}=\frac{y - 3}{x}\); solve for \(y\) to get \(y = 2x + 3\)).
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circle the indefinite pronoun or pronouns that complete each sentence. …
anything ### 91.
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problem 2 estimate the measure of each angle. | angle | measure (degree…
| Angle | Measure (degrees) | |-------|-------------------| | P | $135^\circ$ | | Q | $60^\circ$ | | R | $30^\circ$ | *Note: Estimates may vary slightly (e.g., P could be 120-140°…
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determine the equation of the circle graphed below.
$\boldsymbol{(x+5)^2+(y+2)^2=25}$
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estimate the measure of ∠abc. there are many challenges on this screen.…
60 degrees
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circle whether each underlined pronoun is singular (s) or plural (p). 8…
P ### 85.
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what is the circumference of the circle below? 6 ft
The circumference of the circle is \( 12\pi \) feet (or approximately \( 37.68 \) feet).
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identify all the obtuse isosceles triangles. obtuse isosceles\tnot obtu…
| Obtuse Isosceles | Not Obtuse Isosceles | |------------------------|----------------------------| | First triangle, Fourth triangle | Second, Third, Fifth, Sixth triangles |
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9 - 15. find the measure of each angle. use vocabulary to justify answe…
$m\angle3 = 73^\circ$ (supplementary/linear pair with $\angle2$) $m\angle10 = 107^\circ$ (corresponding angle to $\angle2$) $m\angle9 = 73^\circ$ (supplementary/linear pair with $…
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identify all the obtuse isosceles triangles. obtuse isosceles\tnot obtu…
To solve this, we first recall the definitions: - An **isosceles triangle** has at least two equal sides (marked by tick marks) or two equal angles. - An **obtuse triangle** has o…
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using the pencil, plot the point (-3, 1).
The point $(-3, 1)$ is plotted 3 units left of the origin on the x-axis, then 1 unit up along that vertical line.
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name ______ show all steps!! figures are not drawn to scale! use the fi…
1. C. alternate exterior angles 2. B. corresponding angles 3. F. same side interior 4. E. linear pair 5. H. none of the above 6. G. same side exterior 7. D. vertical angles 8. A. …
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what is the slope of this line? (4, 4) (4, 1) options: 3/4, -3/4, 0, un…
undefined
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using the pencil, plot the point (0, -5).
The point is plotted on the y-axis, 5 units below the origin at the position corresponding to $(0, -5)$.
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find the slope of the line. 5/4 4/5 -4/5 -5/4
\(\frac{4}{5}\) (corresponding to the option "4/5")
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in the figure below, m∠sqp = 128°. (a) write an equation to find x. mak…
\( 60 + 4x = 128 \)
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given the figure below, find the values of x and z.
\(x = 13\), \(z = 118\)
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a system of equations is shown on the graph. how many solutions does th…
Infinitely many (or "infinite" or "an infinite number of")
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what is the missing length in the scaled copy? units 90 × ? = 30 scale …
15
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using the pencil, plot the point (4, 5).
The point $(4, 5)$ is plotted 4 units to the right of the y-axis and 5 units above the x-axis on the coordinate grid.
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some questions... 11. what is the slope of the line y = 5? 12. what is …
11. $0$ 12. Undefined 13. Undefined 14. - Graph of $y=3$: Horizontal line through $(0,3)$; graph of $y=3x$: Straight line through $(0,0)$ with slope 3. - Difference: $y=3$ is a ho…
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given the figure below, find the values of x and z. the figure shows tw…
\(x = 10\), \(z = 62\)