a.
To show:
a.
Answer to Problem 35E
By HL Congruence Theorem.
Explanation of Solution
Given information:
Both spotlights are the same distance from the stage.
Formula used:
The Hypotenuse-Leg Congruence Theorem
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle , then the two triangles are congruent.
Calculation:
According to the question,
There are two triangles
Now,
Statements | Reasons |
H 1. | 1.Given 2. Given 3. Definition of |
L 5. | 5. Reflexive Property of Congruence
6. HL Congruence Theorem |
Therefore, the triangles are congruent by HL Congruence Theorem that states - If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle , then the two triangles are congruent.
Hence proved.
b.
To show: Whether all the four right triangles in the diagram are congruent.
b.
Answer to Problem 35E
Yes, all the four triangles are congruent.
Explanation of Solution
Given information:
Both spotlights are the same distance from the stage.
Formula used:
The Hypotenuse-Leg Congruence Theorem
If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle , then the two triangles are congruent.
Calculation:
According to the question,
There are two triangles
Now,
Statements | Reasons |
H 1. | 1.Given 2. Given 3. Definition of |
L 5. | 5. Reflexive Property of Congruence
6. HL Congruence Theorem |
There are two triangles
Now,
Statements | Reasons |
H 1. | 1.Given 2. Given 3. Definition of |
L 5. | 5. Reflexive Property of Congruence
6. HL Congruence Theorem |
Now,
There are four triangles
Statements | Reasons |
H 1. | 1.Given |
L 5. | 5. Reflexive Property of Congruence |
Also, all the triangles are right triangles .Therefore, by HL Congruence Theorem all the four triangles are congruent.
Hence proved.
Chapter 12 Solutions
BIG IDEAS MATH Integrated Math 1: Student Edition 2016
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