Warm-Up Exercises GUIDED PRACTICE for Example 1 Rewrite the conditional statement in if-then form. 1. All 90 ° angles are right angles. ANSWER If the measure.

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Presentation transcript:

Warm-Up Exercises GUIDED PRACTICE for Example 1 Rewrite the conditional statement in if-then form. 1. All 90 ° angles are right angles. ANSWER If the measure of an angle is 90 °, then it is a right angle 2. 2x + 7 = 1, because x = –3 ANSWER If x = –3, then 2x + 7 = 1

Warm-Up Exercises GUIDED PRACTICE for Example 1 Rewrite the conditional statement in if-then form. 3. When n = 9, n 2 = 81. ANSWER If n = 9, then n 2 = 81.

Warm-Up Exercises GUIDED PRACTICE for Example 2 6. If a polygon is equilateral, then the polygon is regular. Converse: If polygon is regular, then it is equilateral, True Inverse: If a polygon is not equilateral, then it is not regular, True Contrapositive: If a polygon is not regular, then it is not equilateral, False ANSWER

Warm-Up Exercises GUIDED PRACTICE for Example 3 Use the diagram shown. Decide whether each statement is true. Explain your answer using the definitions you have learned. 7. JMF and FMG are supplementary. This statement is true because linear pairs of angles are supplementary. ANSWER

Warm-Up Exercises GUIDED PRACTICE for Example 3 Use the diagram shown. Decide whether each statement is true. Explain your answer using the definitions you have learned. 8. Point M is the midpoint of FH. ANSWER This statement is false because it is not known that FM = MH. So, all you can say is that M is a point of FH

Warm-Up Exercises GUIDED PRACTICE for Example 3 Use the diagram shown. Decide whether each statement is true. Explain your answer using the definitions you have learned. 9. JMF and HMG are vertical angles. ANSWER This statement is true because in the diagram two intersecting lines form 2 pairs of vertical angles.

Warm-Up Exercises GUIDED PRACTICE for Example 3 Use the diagram shown. Decide whether each statement is true. Explain your answer using the definitions you have learned. 10.FH JG ANSWER This statement is false : By definition if two intersect to form a right angle then they are perpendicular. But in the diagram it is not known that the lines intersect at right angles. So you cannot say that FH JG

Warm-Up Exercises EXAMPLE 4 Write a biconditional Write the definition of perpendicular lines as a biconditional. SOLUTION Definition: If two lines intersect to form a right angle, then they are perpendicular. Converse: If two lines are perpendicular, then they intersect to form a right angle. Biconditional: Two lines are perpendicular if and only if they intersect to form a right angle.

Warm-Up Exercises GUIDED PRACTICE for Example Rewrite the definition of right angle as a biconditional statement. Biconditional: An angle is a right angle if and only if the measure of the angle is 90° ANSWER

Warm-Up Exercises Daily Homework Quiz 2. Decide if the statement about the diagram is true. Explain. BD bisects ABC. ANSWER Yes; point D is in the interior of ABC and m ABD = m CBD, so BD bisects ABC

Warm-Up Exercises Daily Homework Quiz Determine whether the statements are good definitions. ANSWER no 4. If an angle is obtuse then its measure is greater than that of an acute angle. ANSWERyes 3. If two angles are supplementary, then the sum of their measures is 180. o