Question

45°-45°-90° triangles

• a 45°-45°-90° triangle is:
• a ______ triangle.
• an __________ triangle.
• a 45°-45°-______° triangle is called an isosceles right triangle.
• the ________ of the isosceles triangle theorem states that if two angles of a triangle are congruent, then the sides opposite the angles are ________.

Explanation:

Step1: Analyze 45°-45°-90° triangle type (right)

A triangle with a 90° angle is a right triangle. So first blank: right.

Step2: Analyze triangle type (isosceles)

Two angles (45° each) are equal, so sides opposite are equal, making it isosceles. Second blank: isosceles.

Step3: Identify the right angle measure

A 45°-45°-90° triangle has a 90° angle. Third blank: 90.

Step4: Recall the isosceles triangle theorem

The Isosceles Triangle Theorem (or Base Angles Theorem) states that if two angles are congruent, sides opposite are congruent. Fourth blank: Isosceles Triangle; Fifth blank: congruent.

Answer:

1. right
2. isosceles
3. 90
4. Isosceles Triangle
5. congruent