Similarity in Right Triangles

Front

What is the definition of similar triangles?

Back

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

Tags

CCSS.HSG.CO.B.6

CCSS.8.G.A.2

Front

What is the geometric mean of two numbers a and b?

Back

The geometric mean is the square root of the product of the two numbers, calculated as √(a*b).

Tags

CCSS.8.EE.A.2

Front

If two triangles are similar, what can be said about their corresponding sides?

Back

The ratios of the lengths of their corresponding sides are equal.

Tags

CCSS.HSG.SRT.A.2

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Tags

CCSS.HSG.SRT.A.2

Front

How do you find the length of a side in similar triangles?

Back

Use the proportion of the lengths of corresponding sides to set up a ratio and solve for the unknown side.

Tags

CCSS.HSG.SRT.A.2

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.

Tags

CCSS.6.G.A.1

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 4 cm and side DE is 8 cm, what is the ratio of their areas?

Back

The ratio of their areas is (AB/DE)² = (4/8)² = 1/4.

Front

What is the simplest radical form of √50?

Back

5√2.

Front

If x is the height of a triangle and the base is 10 cm, what is the area of the triangle if the area is 50 cm²?

Back

Area = 1/2 * base * height; 50 = 1/2 * 10 * x; x = 10 cm.

Tags

CCSS.6.G.A.1

Front

What is the Pythagorean theorem?

Back

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²).

Tags

CCSS.8.G.B.8