Solving similar triangles

Front

What is a similar triangle?

Back

Triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What is the Scale Factor in similar triangles?

Back

The number you multiply by the sides of one triangle to obtain the sides of a similar triangle.

Front

If triangle ABC is similar to triangle DEF, and the length of AB is 10 and DE is 5, what is the scale factor?

Back

The scale factor is 0.5 (or 1:2).

Front

What is the relationship between corresponding angles in similar triangles?

Back

Corresponding angles in similar triangles are equal.

Front

How do you find a missing side length in similar triangles?

Back

Set up a proportion using the lengths of corresponding sides and solve for the missing length.

Front

If triangle XYZ is similar to triangle PQR, and XY = 8, YZ = 12, and PQ = 4, what is the length of QR?

Back

The length of QR is 6.

Front

What is the formula for finding the area of similar triangles?

Back

If the scale factor is k, the ratio of the areas is k².

Front

If two triangles are similar and the lengths of their sides are in the ratio 3:5, what is the ratio of their areas?

Back

The ratio of their areas is 9:25.

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.

Front

What is the importance of corresponding sides in similar triangles?

Back

Corresponding sides are proportional, which allows us to set up equations to find missing lengths.