Activity 1 Determine if each of the following statements is true or false. On a separate sheet of paper, draw a , if it is true. Otherwise draw a ☹️.
1. In a 45°- 45°- 90° triangle, the hypotenuse is twice the length of the legs.
2. If two angles of triangles are congruent, then it is a 45°- 45°- 90° triangle.
3. If two acute angles of a right triangle are congruent, then each measures 45°.
4. In a 30°- 60°- 90° triangle, the hypotenuse is twice the length of the shorter leg.
5. If two sides of a right triangles are not congruent, then it is a 30°- 60°- 90 triangle.
Answers & Comments
Answer:
Here are the correct assessments for each statement:
1. False - In a 45°-45°-90° triangle, the hypotenuse is equal to the square root of 2 times the length of the legs. Draw a ☹️ for this statement.
2. False - Two angles of a triangle being congruent does not necessarily mean it is a 45°-45°-90° triangle. There are other types of triangles with congruent angles. Draw a ☹️ for this statement.
3. False ☹️
If two acute angles of a right triangle are congruent, it does not necessarily mean that each angle measures 45°. In a right triangle, one of the angles is always 90°, and the other two acute angles must add up to 90°. If two of the acute angles are congruent, they must each measure 45° only if the remaining angle is also 45°, resulting in an isosceles right triangle. However, it is possible for the other acute angle to have a different measure, such as 30° and 60°, or any other combination that adds up to 90°.
4. True - In a 30°-60°-90° triangle, the hypotenuse is twice the length of the shorter leg. Draw a , for this statement.
5. False - Not all right triangles with non-congruent sides are 30°-60°-90° triangles. There are other types of right triangles as well. Draw a ☹️ for this statement.
Answer:
7777777x + 7777777x = 15555554x
Step-by-step explanation: