Similar Triangles Quiz

Is line BC parallel to line DE? Choose the best justification.

• Line BC is parallel to line DE because triangle ABC is a dilation of triangle ADE by a scale factor of 7/5 from point A.

• Line BC is parallel to line DE because triangle ABC is a dilation of triangle ADE by a scale factor of 3 from point A.

• Line BC is parallel to line DE because triangle ABC is a dilation of triangle ADE by a scale factor of 2/7 from point A.

• Line BC is not parallel to line DE because there is no dilation that sends triangle ADE to triangle ABC.

Answer explanation

Line BC is parallel to line DE because triangle ABC is a dilation of triangle ADE by a scale factor of 7/5 from point A. Dilation preserves parallelism, confirming the lines are parallel.

Tags

CCSS.HSG.SRT.A.2

CCSS.8.G.A.4

Which diagram shows a dilation of triangle ABC using center P and scale factor of 1/2?

• i.

• ii.

• iii.

• iv.

Answer explanation

The correct choice is iv. A dilation with a scale factor of 1/2 means the new triangle will be half the size of triangle ABC, centered at point P. Diagram iv accurately represents this transformation.

Tags

CCSS.8.G.A.3

What do the properties of dilations tell you about the measure of angle B in the previous question?

Answer explanation

The properties of dilations indicate that angle measures remain unchanged. Therefore, the measure of angle B is the same before and after the dilation, confirming that it retains its original value.

Tags

CCSS.8.G.A.3

Write a sequence of transformations (dilation, translation, rotation, reflection) to take one triangle to the other.

Answer explanation

To transform one triangle to the other, first perform a translation to align their positions, then apply a rotation to match their orientations, and finally, if necessary, a dilation to adjust their sizes.

Tags

CCSS.HSG.SRT.A.2

CCSS.8.G.A.4

Write a similarity statement about the two figures, and explain how you know they are similar.

Answer explanation

The two figures are similar because their corresponding angles are equal and the lengths of their sides are proportional. This indicates that they maintain the same shape but differ in size.

Tags

CCSS.HSG.SRT.B.5

In the diagram, CB'/CB = CA'/CA. What is the length of CB' ?

Answer explanation

Given CB'/CB = CA'/CA, we can use cross-multiplication to find CB'. If CA and CA' are known, we can solve for CB' directly. The length of CB' can be determined using the proportional relationship.

Tags

CCSS.HSG.SRT.A.2

In the diagram, CB'/CB = CA'/CA. What is the length of BA'?

Answer explanation

Given CB'/CB = CA'/CA, we can use the property of similar triangles. This implies that the segments are proportional. If we know the lengths of CB' and CA', we can find BA' using the ratio, leading to BA' = length derived from the proportions.

Tags

CCSS.HSG.SRT.B.4

Kiran dilated triangle PQR using center C and a scale factor of 3 to form triangle P'Q'R'. Select all the statements that must be true about triangle PQR and its image P'Q'R'.

• Angle R is congruent to angle R'

• C'P'/CP = 5

• CQ'/CQ = 4

• P'Q'/PQ = 4

• QR/Q'R' = 4

Answer explanation

Angle R is congruent to angle R' because dilation preserves angles. CQ'/CQ = 4 is true since the scale factor is 3, making CQ' three times CQ, thus CQ' = 3CQ, leading to CQ'/CQ = 4. Other statements are incorrect.

Tags

CCSS.8.G.A.3

What is the length of segment KL? Explain how you know and how the information given in the diagram led to the method you chose.

Tags

CCSS.HSG.SRT.B.5

Amoy wants to know the height of a tree in his neighborhood. He stands 25 feet away from the tree, and places a mirror on the ground so he can see the top of the tree in the mirror. Diego's eyes are 6.5 feet off the ground. The mirror is between Diego and the tree. It is 5 feet from where Diego is standing. How tall is the tree? Describe how you determined the height of the tree.

Answer explanation

To find the tree's height, use similar triangles. The distance from Diego to the mirror is 5 feet, and from the mirror to the tree is 20 feet (25-5). The height of the tree is (6.5 feet * 20 feet) / 5 feet = 26 feet.

Tags

CCSS.HSG.SRT.B.5