Right Triangle Similarity

What is the value of x?

20 units

What is the value of x???

3 over 2 units

What is the length of line segment KJ?

3 over 5 units

In the diagram, the length YZ of is twice the length of AZ? YA is an altitude of ΔXYZ. What is the length of YA?

5 over 3 units

What is the value of a?

5 units

One leg of an isosceles right triangle measures 5 inches. Rounded to the nearest tenth, what is the approximate length of the hypotenuse?

7.1 inches

What is the approximate value of b, rounded to the nearest tenth?

9.4 units

If the altitude of an isosceles right triangle has a length of x units, what is the length of one leg of the large right triangle in terms of x?

x over 2 units

Consider the diagram and the paragraph proof below. Given: Right △ABC as shown where CD is an altitude of the triangleProve: a2 + b2 = c2 Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA. Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA. The proportions and are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as a2 = cf and b2 = ce. Adding b2 to both sides of first equation, a2 = cf, results in the equation a2 + b2 = cf + b2. Because b2 and ce are equal, ce can be substituted into the right side of the equation for b2, resulting in the equation a2 + b2 = cf + ce. Applying the converse of the distributive property results in the equation a2 + b2 = c(f + e). Which is the last sentence of the pr

Because f + e = c, a2 + b2 = c2.

ΔQRS is a right triangle. Select the correct similarity statement.

STR ~ RTQ