Proving Triangles Similar

Front

What is a midsegment in a triangle?

Back

A midsegment is a line segment that connects the midpoints of two sides of a triangle. It is parallel to the third side and its length is half the length of that side.

Front

If QR is a midsegment of triangle WUV, and the length of side WU is 16, what is the length of segment QR?

Back

8 (QR is half the length of WU).

Front

How do you determine the height of an object using similar triangles?

Back

By setting up a proportion between the heights and the lengths of the shadows of the objects.

Front

If Lance the alien is 5 feet tall and his shadow is 8 feet long, what is the ratio of height to shadow length?

Back

5:8.

Front

If a tree's shadow is 32 feet long at the same time as Lance's shadow, what is the height of the tree if the ratio remains the same?

Back

20 feet.

Front

What does it mean for two triangles to be similar?

Back

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

If triangle PQR is similar to triangle XYZ, and the perimeter of triangle PQR is 63 cm, what is the perimeter of triangle XYZ if the ratio of similarity is 2:1?

Back

126 cm.

Front

What is the relationship between the lengths of corresponding sides of similar triangles?

Back

The lengths of corresponding sides of similar triangles are proportional.

Front

If the length of side AB in triangle ABC is 12 cm and the length of side DE in triangle DEF is 18 cm, are the triangles similar?

Back

Yes, if the corresponding angles are equal, the triangles are similar.

Front

What is the measure of x if triangle ABC is similar to triangle DEF and the corresponding sides are in the ratio 3:2?

Back

If the side corresponding to x in triangle DEF is 6 cm, then x = 9 cm.