Question

Interactive Practice: Understand the Pythagorean Theorem and Its Converse
You can use a right triangle with leg lengths a and b and hypotenuse length c to prove the Pythagorean Theorem. Show that a² + b² = c².
Step 1: Make a square with an area of c².
b
a
Why are the corners of the unshaded shape right angles? Complete each sentence.
C
C
b
In each right triangle, the sum of the measures of the two acute angles is ? A
b
45°
C
a
a
b
90°
180°

Answer 1

Fill in the blank: In each right triangle, the sum of the measures of the two acute angles is 90°.

Explanation to complete the sentences:
- Each corner of the unshaded shape is formed by two acute angles from two right triangles.
- Those two acute angles are complementary (their measures add to 90°).
- Therefore each corner of the unshaded shape is a right angle.