Triangle Similarity/Parallel Lines and Proportional Parts

Front

What is Triangle Similarity?

Back

Triangle similarity refers to the property of two triangles having the same shape but possibly different sizes. This means their corresponding angles are equal and their corresponding sides are in proportion.

Front

What does AA stand for in triangle similarity?

Back

AA stands for Angle-Angle similarity criterion, which states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What does SAS stand for in triangle similarity?

Back

SAS stands for Side-Angle-Side similarity criterion, which states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

What does SSS stand for in triangle similarity?

Back

SSS stands for Side-Side-Side similarity criterion, which states that if the three sides of one triangle are in proportion to the three sides of another triangle, then the triangles are 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 the midsegment QR of triangle WUV is 8, what is the length of side WU?

Back

The length of side WU is 16, since the midsegment is half the length of the side it is parallel to.

Front

What is the ratio of the perimeters of two similar figures?

Back

The ratio of the perimeters of two similar figures is equal to the ratio of their corresponding side lengths.

Front

If the width of square J is 28 in and the ratio of the widths of square J to square M is 4:5, what is the width of square M?

Back

The width of square M is 35 in.

Front

How do you find the height of a second road sign using similar triangles?

Back

You can set up a proportion using the heights and shadow lengths of the two signs. If the first sign is 20 ft tall and casts a shadow of 25 ft, and the second sign casts a shadow of 15 ft, the proportion is: 20/25 = height/15.

Front

What is the height of the second road sign if the proportion is set up correctly?

Back

The height of the second road sign is 12 ft.