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Chapter 3: Q1. (page 82)

For each statement

  1. tell whether the statement is true or false,
  2. write the converse,
  3. tell whether the converse is true or false.

If two lines are perpendicular, then they form congruent adjacent angles.

Short Answer

Expert verified
  1. Given statement is true
  2. If two lines intersect to form congruent adjacent angles, then the lines are perpendicular.
  3. Converse statement is true.

Step by step solution

01

Part a. Step 1. Meaning of congruent adjacent angles.

Adjacent angles are angles that come out of the same vertex. Vertical angles are always congruent, which means that they are equal.

02

Part a. Step 2. Meaning of given statement.

When two lines are perpendicular, then they form four angles each measuring90掳

So, all the adjacent angles are congruent.

03

Part a. Step 3. Conclusion.

From first and second statement given statement is true.

04

Part b. Step 1. Converse of a statement.

Converse of a statement 鈥渋f P then Q鈥� is 鈥渋fQ then P鈥�

05

Part b. Step 2. Find P and Q in given statement.

P is 鈥渓ines are perpendicular鈥�

Q is 鈥渃ongruent adjacent angles鈥�

06

Part b. Step 3. Converse of given statement.

If two lines intersect to form congruent adjacent angles, then the lines are perpendicular

07

Part c. Step 1. Meaning of congruent adjacent angles.

Adjacent angles are angles that come out of the same vertex. Vertical angles are always congruent, which means that they are equal.

08

Part b. Step 2. Meaning of converse statement.

The sum of all the angles when two intersect is 360掳. If the adjacent angles are congruent, then the measure of each angle is 90掳. That means, the lines are perpendicular.

09

Part c. Step 3. Conclusion.

From first and second statement given statement is true.

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