To find:whether the given statement is true or false. Also, to write the converse of given statement and to write whether the converse is true or false.
Answer to Problem 26CUR
The given statement is false.
The converse is “If a
The converse is true.
Explanation of Solution
Given information:The given statement is “A triangle is isosceles if it is equilateral”.
First, we will find whether the given statement is true or false.
A triangle is known as an isosceles triangle if it’s any of two legs are equal.
A triangle is said to be equilateral if all of its sides are equal.
Consider the following triangle:
This triangle is not equilateral as all of its sides are not equal. But is it isosceles as its two sides are equal.
So, although the triangle is not equilateral, it is isosceles.
Hence, the given statement is “A triangle is isosceles if it is equilateral” is false.
Now will write the converse of the given statement.
The converse is “If a triangle is equilateral, it is isosceles”
Now will find whether the converse is true or false.
If a triangle is equilateral then all of its sides are equal that is two sides are also equal that is the triangle is isosceles.
So, the converse is true.
Chapter 3 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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