Topic Test 3 & 4 Review Lesson Part 3

​Topic Test 3 & 4 Review Lesson Part 3

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Multiple Choice

In the figure below, p $$\parallel$$ q. Which of these statements is NOT true? #3

• m∠1 = m∠4

• m∠6 = m∠2

• m∠6 + m∠3 = 180°

• m∠2 + m∠5 = 180°

Fill in the Blanks

In the diagram, parallel lines l and k are cut by transversal p. The measure of angle 5 is 138°. What is $m\angle3+m\angle6$   ? *** #23

 

Multiple Select

Which of these angles are congruent to angle 5 and why? (Select all that apply) #24

• Angle 6, Same-Side Interior Angles are congruent

• Angle 8, Vertical Angles are congruent

• Angle 1, Corresponding Angles are congruent

• Angle 4, Alternate Interior Angles are congruent

Match

Consider the following figures given in the first row and match these figures with the correct name for the pair of angles shown in the figure. #26

Alternate interior angles

Alternate exterior angles

Corresponding angles

Vertical angles

• Alternate interior angles

• Alternate exterior angles

• Corresponding angles

• Vertical angles

Properties of Sequences of Rigid Motions

• Size and shape stay the same.

• Angle measures stay the same.

• Area and perimeter stay the same.

• Parallel segments or lines stay parallel.

• Pre-image and image are congruent.

Match

Match each description of a transformation with the corresponding coordinate notation rule. #6

• Translate 3 units to the right and 2 units up.

• Translate 4 units to the left and 2 units down.

• Reflect across the

  𝑦 −axis.

• Rotate 180° about the origin.

(𝑥, 𝑦) → (𝑥 +3, 𝑦 + 2)

(𝑥, 𝑦) → (𝑥 −4, 𝑦 − 2)

(𝑥, 𝑦) → (−𝑥, 𝑦)

(𝑥, 𝑦) → (−𝑥, −𝑦)

• (𝑥, 𝑦) → (𝑥 +3, 𝑦 + 2)

• (𝑥, 𝑦) → (𝑥 −4, 𝑦 − 2)

• (𝑥, 𝑦) → (−𝑥, 𝑦)

• (𝑥, 𝑦) → (−𝑥, −𝑦)

Multiple Choice

****Which best explains whether or not ΔABC ≅ ΔLMN? #32

• The figures are congruent because a 270° rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN.

• The figures are congruent because a 180 rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN.

• The figures are not congruent because point B corresponds with point N and point C corresponds with point M.

• The figures are not congruent because there is no rigid transformation or combination of rigid transformations that will map ΔABC onto ΔLMN.

Multiple Select

What dilation of scale factor can be used to create an image that is CONGRUENT to its pre-image? Check all that apply. #33

• Scale factor of 3.

• Scale factor of 1/3.

• Scale factor or -2.

• Scale factor of 1.

• Scale factor of -1.

Multiple Select

#41

• a translation 1/2 unit up followed by a reflection across the y-axis

• a reflection across the x-axis followed by a rotation of 90 degrees

• a dilation by a scale factor of 2 followed by a translation 5 units left

• a dilation by a scale factor of −1 followed by a reflection across the y-axis

• a dilation by a scale factor of −2 followed by a dilation by a scale factor of 2

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Perpendicular Bisector - Definition, Construction, Properties, Examples | Perpendicular Bisector of Triangle

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Multiple Choice

What type of construction do you see? #30

• midpoint

• angle bisector

• perpendicular bisector

• altitude

Multiple Choice

Eric was attempting to construct a perpendicular bisector to the segment AB with a compass and straight edge. Which of the below statements explains what Eric may have done wrong? #31

• Eric should have started by putting the compass needle point at the midpoint of the segment AB.

• On the second step, Eric should have placed the compass needle point where the first arc intersected the segment AB.

• Erick just needed to open the compass more to create arcs that have a radius of more than half the length of the segment AB.

• Erick didn’t do anything wrong he just needs to connect the opposite endpoints of each arc to finish the construction.

Multiple Select

Which of the following are similarity transformations? Choose all that apply. #14

• Translation

• Dilation

• Rotation

• Stretch

• Reflection

Multiple Choice

Describe the similarity transformation that maps triangle ABC to triangle DEF. #15

• a dilation with a scale factor of 2 followed by a translation 4 units right and 3 units down.

• a dilation with a scale factor of

  1/2 followed by a translation of 4 units left and 3 units up.

• Translation 4 units right and 3 units down followed by a dilation with a scale factor 2.

• Translation 4 units left and 3 units up followed by a dilation with a scale factor 1 / 2.

Multiple Select

Triangle MRT is similar, but not congruent, to triangle ABC. Triangle ABC underwent two transformations to get Triangle LMN. Select two of the following pairs of transformations that could have occurred. #17

• Dilation of 1/2 and a translation of 8 units down

• 90-degree counterclockwise rotation and a dilation of 3.

• Translations of 5 units down and left and a reflection over the x-axis

• Reflection over y=3x+5 and a 180 degree clockwise rotation.

Multiple Select

Select ALL the true statements about an image after a dilation. #18

• The image is a different shape than the preimage.

• The image is a different size than the preimage.

• The image has the same angle measures as the preimage.

• The image is similar to the preimage.

• The image has the same side lengths as the preimage.

Multiple Choice

Given that MON ∼ POQ, and coordinates P(−4, 0), M(−2, 0) and Q(0, −12), find the coordinates of N and the scale factor of POQ to MON. #2

• N (0, −6) and scale factor is 2.

• N (0, −8) and scale factor is $$\frac{2}{3}$$   .

• N (−6, 0) and scale factor is 3.

• N (0, −6) and scale factor is $$1\ \frac{1}{2}$$  

12.1 Triangle Proportionality Theorem

"Winners are not people who never fail but people who never quit."

Corresponding Angles

The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.

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Multiple Choice

What is the definition of the side splitter theorem? #43

• if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides congruently.

• if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally.

• If the three sides of one triangle are congruent to the corresponding sides to another triangle, then the two triangles are congruent.

• If the three sides of one triangle are congruent to the corresponding sides to another triangle, then the two triangles are proportional.

Multiple Select

Line RS intersects triangle BCD at two points and is parallel to segment DC. #44

Which statements are correct? Select three options.

• △BCD is similar to △BSR.

• $$\frac{BR}{RD}=\frac{BS}{SC}$$

• If the ratio of BR to BD is $$\frac{2}{3}$$ , then it is possible that BS = 6 and BC = 3.

• (BR)(SC) = (RD)(BS)

• $$\frac{BR}{RS}=\frac{BS}{SC}$$

Multiple Choice

Use the converse of the side-splitter theorem to determine if   $$TU\parallel RS$$  . Which statement is true? #45

• Line segment TU is parallel to line segment RS because  $$\frac{32}{36}=\frac{40}{45}$$   .

• Line segment TU is not parallel to line segment RS because  $$\frac{32}{36}\ne\frac{40}{45}$$  

• Line segment TU is parallel to line segment RS because  $$\frac{32}{45}=\frac{40}{36}$$   .

• Line segment TU is not parallel to line segment RS because  $$\frac{32}{45}\ne\frac{40}{36}$$   .

Directed Line Segment Formula

Remember to use Order of Operation

Fill in the Blanks

On a coordinate plane, the position of two friends can be defined by the points A(2,5) and B(8,8). Their teacher is standing at point C, the teacher's distance from point A is twice the distance from point B. What is the y coordinate of point C? #25

Multiple Choice

What are the x- and y- coordinates of point E, which partitions the directed line segment from J to K with JP/KP = 2/5? $$x=\left(\frac{m}{m+n}\right)\left(x_2-x_1\right)+x_1;\ y=\left(\frac{m}{m+n}\right)\left(y_2-y_1\right)+y_1$$  #37

• (–13, –3)

• (–7, –1)

• (–5, 0)

• (17, 11)