a.
To show: The additional information to prove
a.
Answer to Problem 23E
The additional information is
Explanation of Solution
Given information:
To support a tree, wires have been attached from the trunk of the tree to stakes in the ground.
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. Definition of |
L 4. | 4.Reflexive Property of Congruence |
The additional information to prove
The hypotenuse should be equal.
Hence, the additional information is
b.
To name: The theorem used to prove
b.
Answer to Problem 23E
The SAS Congruence Theorem is used .
Explanation of Solution
Given information:
To support a tree, wires have been attached from the trunk of the tree to stakes in the ground.
K is the midpoint of JM.
Formula used:
Side-Angle-Side Congruence Theorem
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then two triangles are congruent.
Calculation:
According to the question,
There are two triangles
Now,
Statements | Reasons |
S 1. | Given, K is the midpoint of JM. |
A 2. | Given, |
S 3. | 4.Reflexive Property of Congruence |
4. | SAS Congruence Theorem |
The SAS Congruence theorem is used to prove
Chapter 12 Solutions
BIG IDEAS MATH Integrated Math 1: Student Edition 2016
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