几何
三角形、圆、解析几何与证明题。
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what is the perimeter of the parallelogram? units
20
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first graph the equations, and then mark the point of intersection. $y …
The point of intersection is \((-6, 4)\)
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given ∠x and ∠y are complementary angles. the measure of ∠y is 10° more…
$m\angle Y = 50^\circ$ and $m\angle X = 40^\circ$
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complete the table to show the number of triangles that each polygon ca…
| Number of Sides of the Polygon | Number of Triangles Formed | Interior Angle Sum | |--------------------------------|----------------------------|--------------------| | 12 | 10…
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what is the relationship between $\\angle por$ and $\\angle ros$? \\big…
Supplementary angles
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which triangle is similar to $\\triangle abc$ if $\\sin(a) = \\frac{1}{…
The triangle similar to \(\triangle ABC\) is the triangle with vertices \(I\), \(J\), \(K\) (right - angled, sides \(3\), \(3\sqrt{15}\), \(12\)) (or the triangle \(XYZ\) with sid…
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1. in the figures below, identify as many examples of the terms listed …
To solve this, we analyze each term using circle definitions: ### a. Chord A chord is a line segment with both endpoints on the circle. - $\overline{RS}$: Endpoints $R, S$ on circ…
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use your understanding of triangles to answer the questions below. 8. i…
8. C. $82.8^\circ$ 9. $58.2^\circ$
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consider △abc. what are the angles that make the trigonometric statemen…
For \(\sin(\underline{?})=\cos(B)\), the angle is \(A\); for \(\sin(B)=\cos(\underline{?})\), the angle is \(A\)? Wait, no, wait the first blank: \(\sin(A)=\cos(B)\), the second b…
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m∠e = 104°; m∠f = 96° are the two angles complementary, supplementary, …
neither
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use your understanding of triangles to answer the questions below. 8. i…
8. C. $82.8^\circ$ 9. $58.2^\circ$
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6 solve the system of equations below by graphing each line on the coor…
The solution of the system is the point \((2,1)\)
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m∠c = 97°; m∠d = 83° are the two angles complementary, supplementary, o…
supplementary
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determining a tangent ratio what is the value of \\(\\tan(60^{\\circ})\…
$\boldsymbol{\sqrt{3}}$ (corresponding to the option with $\sqrt{3}$)
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express (sin g) as a fraction in simplest terms.
\( \frac{3}{5} \)
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m∠a = 72°; m∠b = 18° are the two angles complementary, supplementary, o…
Complementary
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what is the measure of the supplement of the angle? 3° enter your answe…
$177^\circ$
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use the diagram of triangle xyz to answer the questions. what is the le…
s: - Length of side XY: \(10\) - \(\sin(X)\): \(\frac{4}{5}\) - \(\cos(X)\): \(\frac{3}{5}\) - \(\tan(X)\): \(\frac{4}{3}\)
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what is the measure of the complement of the angle? 62° enter your answ…
$28^\circ$
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determining the sine ratio what additional information would be necessa…
C. The length of BC is needed because it is the side opposite \(\angle\)A.
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what is the measure of the supplement of the angle? 142° enter your ans…
$38$
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what is the measure of the supplement of the angle? 62° enter your answ…
$118^\circ$
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the measure of angle a is 5 times the measure of its supplement. what i…
The measure of angle A is $150^\circ$. The measure of its supplement is $30^\circ$.
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example 1: find the sum of the measures of the interior angles of the i…
\( 1260^{\circ} \) #### b) Dodecagon (12 - sided polygon)
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$\\angle g$ and $\\angle h$ are complementary angles. the measure of $\…
$m\angle G = 41^\circ$ $m\angle H = 49^\circ$
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bc = round your answer to the nearest hundredth.
$4.92$
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2x + 4y = 8 2y = 3x - 12 **choose the correct line to graph: line 1 is …
To graph \(2x + 4y = 8\) (rewritten as \(y=-\frac{1}{2}x + 2\)), use the line (e.g., Line AB) passing through \((0,2)\) and \((4,0)\). To graph \(2y = 3x-12\) (rewritten as \(y=\f…
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2x + 4y = 8\ 2y = 3x - 12\ **choose the correct line to graph: line 1 i…
If the equation to graph is \(2x + 4y = 8\), the correct line is Line AB. If the equation to graph is \(2y=3x - 12\), the correct line is Line CD. (If we assume the question is to…
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solve the problem. use what you learned from the model. von makes a des…
### Step 1: Draw the Diagram Let's assume two parallel lines \( a \) and \( b \), and two transversal lines \( c \) and \( d \). So we have: - Line \( a \) (top parallel line) - L…
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estimate solutions to systems of equations graphically determine the nu…
1. **How many solutions?** one at $(-2, 2)$ **How do you know?** Lines intersect once. 2. **How many solutions?** none **How do you know?** Lines are parallel, no overlap. 3. **Ho…
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one pair of angles in your map to illustrate each angle relationship me…
For example, \( \angle 1 \) and \( \angle 5 \) are corresponding angles (if \( m \parallel n \)) and are equal. \( \angle 1 \) and \( \angle 3 \) are vertical angles and equal. \(…
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consider parallelogram pqrs below. note that pqrs has vertices ( p(-3, …
### (a) Length of $\overline{PQ}$: $\boldsymbol{\sqrt{53}}$ Length of side adjacent to $\overline{PQ}$: $\boldsymbol{\sqrt{53}}$ ### (b) Slope of $\overline{PQ}$: $\boldsymbol{\fr…
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4. which geometric sequence has a first term equal to 55 and a common r…
{55; -275; 1,375; -6,875; ...}
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which angles are corresponding angles? ∠qpn and ∠qps ∠qpn and ∠rsu ∠qpn…
$\angle QPN$ and $\angle RSU$ (the option with $\angle QPN$ and $\angle RSU$)
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a flat screen television is advertised as being 46 inches on its diagon…
40.4
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a rectangular park is x feet long and y feet wide. the new design of th…
The perimeter of the redesigned park (including the pathway) is \( 2.74x + 2.24y+56 \) feet.
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fill in the blanks to complete the sentences. then find the measures of…
2 pairs of corresponding angles: \(a\) and \(b\), \(c\) and \(d\) If \(AB \parallel CD\), then \(a = b\) and \(c = d\) ### Part 2: Alternate Angles
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which angles are supplementary angles? ∠ijh and ∠nmo ∠ijh and ∠kjh ∠ijh…
\(\boldsymbol{\angle IJH}\) and \(\boldsymbol{\angle KJH}\) (the option: \(\angle IJH\) and \(\angle KJH\))
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bus below, find the measures of $\\angle 1$, $m\\angle 1$ $m\\angle 2$ …
$m\angle 1 = 42^\circ$ $m\angle 2 = 48^\circ$ $m\angle 3 = 42^\circ$ $m\angle 4 = 48^\circ$
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(b) what is the solution?
(3, 0)
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are ∠3 and ∠5 congruent? explain.
Assuming a typical diagram (e.g., vertical angles or parallel lines with a transversal), \(\angle3\) and \(\angle5\) are congruent. The reason is that vertical angles are congruen…
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answer the parts below. (a) plot 3 and 2 on the number line below. (b) …
3 is located to the right of 2 (the option with this text, e.g., if it was option B, then B. 3 is located to the right of 2) ### Part (C)
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find the perimeter and area of the right triangle shown below. 13 cm 10…
Perimeter = 31.31 cm Area = 41.55 $\text{cm}^2$
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9 you are solving a system of two linear equations in two variables, an…
A. Blue
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find the measures of angles 3, 8, 9, and 14 to show that the sum of the…
The angles are \(\frac{540}{17}^\circ\) (or \(\approx31.76^\circ\)), \(\frac{1440}{17}^\circ\) (or \(\approx84.71^\circ\)), \(\frac{1620}{17}^\circ\) (or \(\approx95.29^\circ\)), …
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9 you are solving a system of two linear equations in two variables, an…
A. Blue
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what is the minimum length the ladder must be to reach the roof? round …
4.5
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what is the area of the quadrilateral shown below? 7 25 4
132
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8 you are solving a system of two linear equations in two variables, an…
B. Green
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in the figure shown, which composition of rigid transformations will ma…
B. a reflection followed by a translation
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solve. use the diagram shown to solve problems 3–5. 3 in the diagram, l…
s: - \(m\angle 2 = \boldsymbol{115^\circ}\) (supplementary angles) - \(m\angle 5 = \boldsymbol{65^\circ}\) (alternate interior angles) - \(m\angle 13 = \boldsymbol{100^\circ}\) (c…
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solve the inequality and graph the solution. \\(\frac{x}{2} - 1 > 1\\) …
The solution to the inequality is $x > 4$. For the graph: Place an open circle at 4 on the number line, and draw a ray extending to the right from this open circle.
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what is the value of ( mangle dae ) and ( mangle dac )? ( circ ) ( mang…
$m\angle DAE = 45^\circ$ and $m\angle DAC = 135^\circ$ (the first option)
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figure c 8.8, x, 14.72 x = figure d x, 4, 10.25 x =
For Figure C: $5.92 < x < 23.52$ For Figure D: $6.25 < x < 14.25$ *Note: If the triangles are right triangles (no right angle indicated), but if we assume the longest side is the …
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solve. use the diagram shown to solve problems 3–5. 3 in the diagram, l…
### Problem 3 #### Step 1: Find \( m\angle 2 \) \(\angle 2\) and \(\angle 3\) are supplementary (linear pair), so \( m\angle 2 + m\angle 3 = 180^\circ \). Given \( m\angle 3 = 65^…
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what is the relationship between $\\angle poq$ and $\\angle tos$? \\big…
Vertical angles
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10. who was euclid, and why is he important?
Euclid was an ancient Greek mathematician. He is important for writing "Euclid's Elements", a work that systematized geometry with axiomatic - deductive methods, laying foundation…
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finding a missing side using the pythagorean theorem find the missing s…
Figure A: $x = 3.6$ Figure B: $x \approx 13.60$
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solve the inequality and graph the solution. 10 + 9c > 1 to draw a ray,…
The solution to the inequality is $c > -1$. For the graph: plot an open circle at $-1$ on the number line, then draw a ray extending to the right from this point.
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find the length of the leg x of the right triangle shown below. x = \\b…
12.450 cm
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solve the inequality and graph the solution. 3z - 8 > 10 to draw a ray,…
The solution to the inequality is $z > 6$. For the graph: place an open circle at 6 on the number line, and draw a ray extending to the right from this open circle.
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on your own: pairs of angles enter your answer in the box. (8x - 7)° (1…
$45$
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enter your answer in the box. check answer
$110$
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enter your answer in the box. check answer
110
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on your own: pairs of angles enter your answer in the box. check answer…
$130$
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find an equation of the vertical line through (0, -4). the equation is …
$x = 0$
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example in the diagram, lines w, x, and y are parallel. use the terms c…
corresponding angles: $\boldsymbol{\angle 3}$ and $\boldsymbol{\angle 7}$ (or other valid pairs like $\angle 5$ and $\angle 9$, $\angle 2$ and $\angle 10$ etc.) alternate interior…
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guided practice see example 1 ( \triangle xyz sim \triangle pqr ) in ea…
1. $a = 15$ cm, $y = 18$ cm 2. $y = 56$ m, unknown side $= 40$ m 3. 28 ft 4. 24.94 ft (rounded) 5. $x = 18$ in 6. $b = 7.2$ ft 7. 3.9 ft 8. ~9 ft 9 in (or 116.67 in)
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5 solve the system of linear equations by graphing. (3 pts) $x + 3y = 6…
The solution to the system of linear equations is \(x = 3,y = 1\) or the ordered pair \((3,1)\)
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1. p and q are points on ab and bc respectively of δ abc. pq || ac. ac …
\( 13.5 \) cm ### Problem 2
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place the six square roots by dragging their dots.
Place the dots representing the square roots at their respective approximate positions on the number line (e.g., \(\sqrt{1}\) at \(1\), \(\sqrt{4}\) at \(2\), etc.). The exact pla…
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vertical angles have the same measure. $m\\angle3 = m\\angle1$ what is …
$m\angle 2 + m\angle 3 = 180^\circ$ Equation to find $m\angle 2$: $m\angle 2 + 62^\circ = 180^\circ$
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determine the perimeter and area of the shape shown below. (both rounde…
Perimeter: $6\pi + 12$ (or approximately 30.85 inches) Area: $9\pi + 36$ (or approximately 64.27 square inches)
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solve. 4 in the diagram, \\(\\overrightarrow{ea} \\perp \\overrightarro…
\(x = 25\) ### Problem 5
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2. a rectangular backyard is x feet long and y feet wide. the new desig…
\( 2.7x + 2.4y + 64 \)
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determine whether the triangle with the given side length is a right tr…
s: - Problem 17: Yes (it is a right triangle) - Problem 18: Yes (it is a right triangle) - Problem 19: No (it is not a right triangle) - Problem 20: No (it is not a right triangle)
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date 02/2/26 period 3 draw a graph for each inequality. 1) ( x < -3 ) 2…
1. Open circle at $-3$, shade all values left of $-3$ 2. Closed circle at $2$, shade all values right of $2$ 3. Open circle at $2$, shade all values right of $2$ 4. Closed circle …
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the base of a solid oblique pyramid is an equilateral triangle with a b…
14 units
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a solid oblique pyramid has a square base with an edge length of 2 cm. …
$4.8$ cm³ (Option C: $4.8\ \text{cm}^3$)
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which lengths can be used, directly or indirectly, to calculate the vol…
- XY and ST - VU and TW - TX and WX
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18. evaluate: (+2)(-3) - (-4)(-5) - (+6) 20. find the perimeter and are…
\(-32\) ### Question 20
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a solid oblique pyramid has an equilateral triangle as a base with an e…
$16\sqrt{3}$ cm³ (Option B)
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a solid right pyramid has a square base. the base edge length is 2 cm l…
128 cm³
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19. find the perimeter and area of this parallelogram. dimensions are i…
Perimeter: \( 68 \) millimeters, Area: \( 272 \) square millimeters
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calculating the volume of an oblique pyramid the area of the base of th…
The height, AB, is 6 cm. The volume of the pyramid is 100 cm³.
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writing the volume as an algebraic expression a right pyramid with a sq…
$\frac{x^2(x+2)}{3}$ cubic inches
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3. the slope of the line determined by a (2, -3) and b (-1, 3) is a) -2…
a) -2
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determining when the volumes of pyramids are the same if two pyramids h…
The areas of the bases must be the same.
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what angle is more than 180 degrees and less than 360 degrees? right ob…
E. Reflex ### Second Question:
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2. 10 ft 6 ft 7 ft 12 ft perimeter: area:
Perimeter: \(29\) ft Area: \(36\) square feet
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1. 12 cm 20 cm 16 cm perimeter: area:
Perimeter: \(48\) cm Area: \(96\) cm²
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six identical square pyramids can fill the same volume as a cube with t…
The height of each pyramid is $\frac{1}{2} h$ units.
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practice calculating the volume of right and oblique pyramids. six iden…
The height of each pyramid is $\frac{1}{2}h$ units.
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1. the rectangular floor has a length of 14 meters and a width of 11 me…
The perimeter of the room is 50 meters. ### Question 2
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10) △nop ≅△ __ by ____ △nop ≅△...
\( \triangle NOP\cong\triangle \boldsymbol{NPQ} \) by \(\boldsymbol{HL}\) (or \( \triangle NOP\cong\triangle \boldsymbol{NQP} \) by \(\boldsymbol{SAS}\))
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2. the perimeter of this pentagon is 52 cm. what is the missing length?…
B. 8 cm ### Question 3
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7) $\\triangle abd \\cong \\triangle \\underline{cdb}$ by ______ 8) $\\…
\( \triangle ABD\cong\triangle \boldsymbol{CDB} \) by \(\boldsymbol{SSS}\) (or if angle - side - angle, but SSS is more likely here) ### Problem 8
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4) $\triangle noq cong \triangle$ ___ by ____ 5) $\triangle utr cong \t…
\( \triangle NOQ \cong \triangle \boldsymbol{PQO} \) by \(\boldsymbol{SSS}\) ### Problem 5
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3. a picture frame is 5 cm long and 4 cm wide. how many square centimet…
20 square centimeters ### Question 4
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3. a picture frame is 5 cm long and 4 cm wide. how many square centimet…
The area of the picture frame is \( 20 \) square centimeters.