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.
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
Verified answer
Answer:
Activity 1:
1. False (draw ☹️) - In a 45°-45°-90° triangle, the length of the hypotenuse is √2 times the length of the legs, not twice.
2. False (draw ☹️) - Two congruent angles in a triangle do not necessarily imply a 45°-45°-90° triangle. There are other types of triangles with congruent angles.
3. False (draw ☹️) - Two congruent acute angles in a right triangle can have different measures, not necessarily 45°. They could be any two equal acute angles.
4. True (draw ) - In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg.
5. False (draw ☹️) - A right triangle with non-congruent sides does not necessarily imply a 30°-60°-90° triangle. There are other possibilities for right triangles with non-congruent sides.
Answer:
Activity 1:
1. False (draw ☹️) - In a 45°-45°-90° triangle, the length of the hypotenuse is √2 times the length of the legs, not twice.
2. False (draw ☹️) - Two congruent angles in a triangle do not necessarily imply a 45°-45°-90° triangle. There are other types of triangles with congruent angles.
3. False (draw ☹️) - Two congruent acute angles in a right triangle can have different measures, not necessarily 45°. They could be any two equal acute angles.
4. True (draw ) - In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg.
5. False (draw ☹️) - A right triangle with non-congruent sides does not necessarily imply a 30°-60°-90° triangle. There are other possibilities for right triangles with non-congruent sides.
Step-by-step explanation: