Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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reasoning about definitions and properties of geometric figures determi…
always ### Question 2: Perpendicular lines are $\boldsymbol{ ule{1cm}{0.15mm}}$ coplanar.
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apply: circle problem #4 point o is the centre of the circle. what is t…
\(80\)
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the point a is shown below. reflect a across the x - axis. then reflect…
The final point is (0, - 6), so we plot the point with coordinates (0, - 6) on the graph.
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given ( m parallel n ), find the value of ( x ). answer attempt 1 out o…
\( x = 17 \)
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calculate the area and perimeter(all around). perimeter: ____ ft area: …
Perimeter: 112 ft Area: 488 ft²
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11. find the intersection of the line\\(vec{r}(t) = langle -1, 0, 1 ang…
The intersection point is $\langle 1, 2, 3 angle$
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10. if m is the midpoint of segment ab and if am = 6x - 8 and mb = 3x +…
46
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select the correct answer. heather’s work to find the distance between …
A. She substituted incorrectly into the distance formula.
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select the correct answer. brian sets up the distance formula to find t…
A. He subtracted the coordinates instead of adding them to get the distance terms.
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determining the vertex of a parabola from its graph what is the vertex …
\((-3, - 4)\)
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(a) graph the system. (b) use your graph to estimate the solution to th…
$(1.5, 0.5)$
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15c: choose two directions: choose two words that best explain or defin…
1. November: b. month, d. ninth 2. nonagon: a. polygon, c. nine 3. decade: b. years, c. ten 4. decimeter: a. metric, c. ten 5. decimal: b. ten, c. part 6. century: a. 1,000, b. 10…
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select the correct answer. fernando is using the distance formula to fi…
He subtracted the wrong coordinates to find the distance of the horizontal leg.
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4) translation: $(x, y) \ ightarrow (x + 3, y - 5)$
To solve the translation of the vertices (assuming we need to find the translated coordinates of points like \( V \), \( F \), and the other vertex, let's first identify the coord…
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question 3 of 3 select the correct answer. jason and caleb walk from th…
1,523 meters
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modeling real life a pile is a post - like support made of timber, stee…
About 4 feet 4 inches
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select the correct answer. gradys father is building a 15 - meter fence…
(-1,-7)
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b) rotate △abc 180° around the origin.
The coordinates of the rotated triangle \( \triangle A'B'C' \) are \( A'(-1,0) \), \( B'(-2,-3) \), and \( C'(-3,0) \). To graph it, plot these points and connect them.
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translations which statements are true about triangle abc and its trans…
To solve this, we analyze the translation of triangle \( ABC \) to \( A'B'C' \) by looking at the coordinates of a vertex (e.g., \( A(-1, 3) \) to \( A'(2, -2) \)): ### Step 1: An…
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△jkl is rotated 90° clockwise around the origin to form △jkl. 90° clock…
\( (5, -7) \)
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hw- 2.6 part2 score: 6.65/20 1/2 answered question 2 solve the followin…
The solution to the inequality \(|2x - 3| + 1 < 6\) is \(-1 < x < 4\). To graph the solution set, we draw an open circle at \(x = -1\) and \(x = 4\) (since the inequality is stric…
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in the diagram, which is not drawn to scale, g is the incenter of $\\tr…
$21$
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4. the length of a rectangle is eight more than twice its width. the pe…
- Variable: Let \( w \) be the width (in feet), length \( l = 2w + 8 \) - Equation: \( 88 = 2((2w + 8) + w) \) - Solution: Width \( w = 12 \) feet, Length \( l = 32 \) feet
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in the figure below, suppose ( mangle1 = 67^circ ) and ( mangle3 = 56^c…
### Step 1: Sum of interior angles of a triangle The sum of the interior angle measures of a triangle is a well - known geometric fact. By the triangle angle - sum theorem, the su…
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the sum of the interior angle measures of a triangle must be 180°. so, …
\( m\angle2 = m\angle1 + m\angle4 \) (so the symbol in the box should be \( = \))
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which coordinate is the same as the x - coordinate of point m? x - coor…
y - coordinate of point M
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in the figure below, suppose ( mangle 1 = 37^circ ) and ( mangle 4 = 10…
s: - The sum of the interior angle measures of a triangle must be \(\boldsymbol{180}\)°. - \(m\angle1 + m\angle3 + m\angle4=\boldsymbol{180}\)°. - \(m\angle1 + m\angle4=\boldsymbo…
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15a: sentence completion directions: complete the following sentences w…
1. century 2. percent 3. nonagon 4. decade 5. November 6. decimal 7. centigrade 8. centenarians 9. century 10. decimeter --- ### 15B: Yes or No?
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determine whether the following statement is true or false. if it is fa…
B. False. If the points are collinear, then the perpendicular bisectors will be parallel and thus, won't intersect. Therefore, a circumscribed circle won't be possible.
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quadrilateral qrst is an isosceles trapezoid, $qs = 3b - 82$, and $rt =…
\( 82 \)
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ux is the midsegment of the trapezoid stvw. if vw = 48z - 80, ux = 41z …
\( z = 2 \)
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1. essential question what angle relationships are created when paralle…
When parallel lines are intersected by a transversal, the angle relationships include: equal corresponding angles, equal alternate interior angles, equal alternate exterior angles…
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find the missing angle measures. name: ∠2 = 68° ∠3 = 36° ∠1 = 100° ∠4 =…
∠1 = \(100^\circ\), ∠2 = \(68^\circ\), ∠3 = \(36^\circ\), ∠4 = \(20^\circ\), ∠5 = \(68^\circ\), ∠6 = \(130^\circ\)
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the longest side of an acute triangle measures 30 inches. the two remai…
72.4 in.
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which best explains whether a triangle with side lengths 2 in, 5 in, an…
The triangle is not acute because $2^{2}+4^{2}<5^{2}$.
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arielle is building the wooden framework for the roof of a house. she n…
B. It is an obtuse triangle. About 0.8 foot needs to be removed from the 20-foot board to create a right triangle.
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an acute triangle has two sides measuring 8 cm and 10 cm. what is the b…
6 < s < 12.8
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the longest side of an acute isosceles triangle is 12 centimeters. roun…
D. 8.5 cm
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the longest side of an obtuse triangle measures 20 cm. the two shorter …
6.3
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suppose that e and f are points on the number line. if ef=13 and e lies…
-10, 16
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which set of numbers can represent the side lengths, in centimeters, of…
10, 24, 26
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the shorter sides of an acute triangle are x cm and 2x cm. the longest …
B. 7
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which set of numbers can represent the side lengths, in inches, of an a…
B. 5, 7, 8
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which classification best represents a triangle with side lengths 6 cm,…
obtuse, because $6^2 + 10^2 < 12^2$
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explaining triangle classification theorems your classmate is unsure ab…
To classify a triangle by its side lengths, follow these steps: 1. Sort the sides as $a \leq b \leq c$, where $c$ is the longest side. 2. **By side equality**: - Equilateral: $a =…
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applying triangle classification theorems to get from his house to the …
Lin walked southwest, creating an obtuse triangle.
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the corresponding angles of similar figures are ______. proportional th…
the same (the option: the same)
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scale factors similar figures are figures that have the same ______. nu…
D. shape
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directions: find the slope of 1.
The slope of the line is \(1\).
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identifying possible side lengths marlena has 3 straws. two straws have…
A. 5 inches, B. 6 inches
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identifying possible side lengths marlena has 3 straws. two straws have…
5 inches, 6 inches
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applying the converse of the pythagorean theorem janice examines the gi…
It is over by approximately 0.6 units.
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on the packaging for a triangular sail, the edge measurements for the s…
obtuse
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ellas geometry teacher asked each student to devise a problem and write…
Ella's procedure and conclusion are incorrect.
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which value from the list below, when substituted for x, would represen…
14
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apply: circle problem #3 point o is the centre of the circle. what is t…
\( 80^\circ \) (Wait, no, maybe 40. Wait, I'm confused. Let's start over. The key is: \( OA = OB \) (radii), so \( \triangle OAB \) is isosceles. \( \angle OAB = 50^\circ \), so \…
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which sets of three of numbers represent the sides of an obtuse triangl…
2, 2, 3 3, 5, 6
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apply: finding unknown angle measures two angles, ∠1 and ∠2, are comple…
The measure of $\angle 1$ is $61^\circ$, and the measure of $\angle 2$ is $29^\circ$.
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calculate the perimeter of the given irregular shape. type only the num…
30
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calculate the area of the given irregular shape. type only the number v…
84
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solving a real - world problem you are told that in a billiards shot, t…
10
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apply: finding unknown angle measures railroad tracks cross park avenue…
B. \(40^\circ\)
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lesson 7: dilations in the coordinate plane second slide - 2/4/26 a (1,…
\( 5 \)
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calculate the perimeter of the following irregular shape. type only the…
46
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calculate the perimeter of the following irregular shape. type only the…
48
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7) what is the value of ( w ) in the figure above? (a) ( 90 ) (b) ( 100…
(C) 110
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applying the triangle inequality theorems and the converse of the pytha…
Triangle JKL is obtuse triangle. Triangle XYZ is acute triangle.
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question 7 of 8 (1 point) | question attempt: 1 of 3 suppose that △ijk …
\( m\angle I = 54^\circ \), \( m\angle J = 72^\circ \), \( m\angle K = 54^\circ \)
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calculate the area of a square whose diagonal is 10 cm. type only the n…
50
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find the unknown measure of the rectangle. area = 63 square feet 7 ft f…
9 feet
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find the area of the parallelogram. 18 in. 19 in. 13.5 in. area = \\squ…
243 in.$^2$
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in the figure above, if ( x = 70 ) and ( y = 40 ) and the dotted lines …
E) 55
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applying the acute triangle inequality theorem use the drop - down menu…
$4^2$ is $\boldsymbol{less\ than}$ $3^2 + 3^2$. Therefore, $\triangle JKL$ is $\boldsymbol{an\ acute\ triangle}$. $5^2$ is $\boldsymbol{equal\ to}$ $3^2 + 4^2$. Applying the same …
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#9 calculate the area of the colored shape: 9cm 6cm 4cm 7cm #1 42 in² #…
$26$ $\text{cm}^2$
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in the figure above, $overline{ad}$, $overline{be}$, and $overline{cf}$…
(A) $40^\circ$
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#7 calculate the area of the colored shape: (image of a blue l - shaped…
$11$ $\text{ft}^2$
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area of composite shapes solve and type your answers into the #6 calcul…
$87$ $\text{yd}^2$
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area of composite shapes #4 calculate the area of the colored shape: 11…
$79$ yd²
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choose the most appropriate letter. show work 1) in the figure above, i…
C) 117
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1. what is the sum of the measures of the interior angles 2. what is th…
s: 1. The sum of interior angles of a polygon is \((n - 2)\times180^{\circ}\) (where \(n\) is the number of sides). 2. The sum of interior angles of a 25 - gon is \(4140^{\circ}\)…
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applying the converse of the pythagorean theorem max has sticks of leng…
6 in., 8 in., and 10 in.
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area of composite shapes #1 calculate the area of the colored shape: 9i…
$42$ $\text{in}^2$
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given: △abc with (a^2 + b^2 = c^2) and right △def constructed with legs…
1. First blank: Pythagorean theorem 2. Second blank: SSS Congruence Postulate 3. Third blank: \(\angle C\) 4. Fourth blank: definition of a right triangle
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8. reasoning is triangle abc a reflection of triangle abc across the li…
No, triangle A'B'C' is not a reflection of triangle ABC across the line. A reflection would create a mirror image where each vertex of ABC is mirrored across the line to form A'B'…
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5. name the transformation or sequence of transformations that map one …
## First Set (ΔDEC): Transformations: A rotation about the origin at **90° clockwise** Followed by a translation of **0 units (no translation needed)** $\Delta DEC \cong \Delta GH…
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applying the pythagorean theorem what is the value of x? x = 10 8
6
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what is the area of square uvwx? area = \\square square units
169 square units
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Question was provided via image upload.
a. \( w = 99^\circ \), because \( 42 + 39 = 81 \) and \( 180 - 81 = 99 \) ### Problem 5
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for each part below, use the figure to fill in the blank. if necessary,…
\( 25 \) ### Part (b)
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7.2 assignment possible points: 0.74 triangles rst and wxy are similar.…
Longest side = 30 inches Second longest side = 21 inches
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$\\overline{wy}$ is an altitude in triangle $wxz$. if $\\triangle ywz \…
$\angle XWZ$ is a right angle.
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suppose the radius r is 2 units and the angle \\(\\theta\\) is \\(120^\…
\( 4.19 \)
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why is the information in the diagram enough to determine that $\\trian…
because $\angle$MNL and $\angle$ONP are congruent angles
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parallelogram fghj was dilated and translated to form similar parallelo…
4
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consider the two triangles. to prove that the triangles are similar by …
$\boldsymbol{\frac{AC}{GI} = \frac{BC}{HI}}$
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numeric 1 point suppose the radius r is 2 units and the angle \\(\\thet…
\( 4.19 \)
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suppose the radius r is 2 units and the angle θ is 120°. what is the ar…
\( 4.19 \)
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exit ticket draw, label and annotate (with all 6 pairs of congruent mar…
1. $\angle A \cong \angle I$ 2. $\angle Y \cong \angle J$ 3. $\angle W \cong \angle P$ 4. $\overline{AY} \cong \overline{IJ}$ 5. $\overline{YW} \cong \overline{JP}$ 6. $\overline{…
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triangle abc was dilated using the rule $d_{r, \\frac{5}{4}}$. if $ca =…
10 units
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name: practice & problem solving 7 leveled practice trapezoid abcd is s…
### Preimage Points: $A=(2, 8)$ $B=(6, 8)$ $C=(8, 3)$ $D=(2, 3)$ ### Image Points (reflection over y-axis): $A'=(-2, 8)$ $B'=(-6, 8)$ $C'=(-8, 3)$ $D'=(-2, 3)$ *(To complete the t…