7-4 Right Triangle Similarity

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Tags

CCSS.4.G.A.2

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².

Tags

CCSS.8.G.B.7

Front

What does it mean for triangles to be similar?

Back

Triangles are similar if they have the same shape but not necessarily the same size. This means their corresponding angles are equal and their corresponding sides are in proportion.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

How can you determine if two triangles are similar?

Back

Two triangles can be determined to be similar if they satisfy one of the following criteria: AA (Angle-Angle), SSS (Side-Side-Side), or SAS (Side-Angle-Side).

Tags

CCSS.HSG.SRT.B.5

Front

What is the relationship between the sides of similar triangles?

Back

The corresponding sides of similar triangles are proportional, meaning the ratios of the lengths of corresponding sides are equal.

Tags

CCSS.HSG.SRT.A.2

Front

If two triangles are similar, how do you find the length of a missing side?

Back

To find a missing side in similar triangles, set up a proportion using the lengths of the corresponding sides and solve for the unknown.

Tags

CCSS.HSG.SRT.A.2

Front

What is the scale factor in similar triangles?

Back

The scale factor is the ratio of the lengths of corresponding sides of two similar triangles.

Tags

CCSS.7.G.A.1

Front

If triangle ABC is similar to triangle DEF, and the lengths of sides AB and DE are 4 and 8 respectively, what is the scale factor?

Back

The scale factor is 1:2, since 4/8 = 1/2.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

How do you apply the Pythagorean theorem to find the length of a side in a right triangle?

Back

To find the length of a side, rearrange the Pythagorean theorem formula: c² = a² + b². If you know two sides, you can solve for the third.

Tags

CCSS.8.G.B.7

Front

What is the value of x if the sides of a right triangle are 9 and 12?

Back

Using the Pythagorean theorem: x² = 9² + 12²; x² = 81 + 144; x² = 225; x = 15.

Tags

CCSS.8.G.B.7