Similar Triangles Quiz
Authored by Grace Smythe
Mathematics
10th Grade
CCSS covered
Used 6+ times
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13 questions
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1.
MULTIPLE CHOICE QUESTION
10 mins • 1 pt
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
2.
MULTIPLE CHOICE QUESTION
10 mins • 1 pt
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
3.
OPEN ENDED QUESTION
10 mins • 1 pt
What do the properties of dilations tell you about the measure of angle B in the previous question?
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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
4.
OPEN ENDED QUESTION
10 mins • 1 pt
Write a sequence of transformations (dilation, translation, rotation, reflection) to take one triangle to the other.
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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
5.
OPEN ENDED QUESTION
10 mins • 1 pt
Write a similarity statement about the two figures, and explain how you know they are similar.
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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
6.
OPEN ENDED QUESTION
10 mins • 1 pt
In the diagram, CB'/CB = CA'/CA. What is the length of CB' ?
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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
7.
OPEN ENDED QUESTION
10 mins • 1 pt
In the diagram, CB'/CB = CA'/CA. What is the length of BA'?
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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
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