Definition: If two lines are perpendicular, then they form right angles. segments. 3. If two angles are right angles, then they are congruent
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1 Notes Page notes Thursday, September 18, :42 PM efinition: If two lines are perpendicular, then they form right angles. Example1: Given : Pr ove : Given 2. is a right angle is a right angle 2. y definition of perpendicular segments If two angles are right angles, then they are congruent
2 Notes Page 2
3 Notes Page notes Wednesday, September 17, :31 PM efinition: If two angles are complementary, then the sum of the two angles is 90 degrees.(right angle) efinition: If two angles are supplementary, then the sum of the two angles is 180 degrees.(straight angle) Note: x = angle 90 - x = complement of an angle x = supplement of the angle Example 1: The measure of one of two complementary angles is three greater than twice the measure of the other. Find the measure of each angle. Example 2: The measure of the supplement of an angle is sixty less than three times the measure of the complement. Find the measure of the complement.
4 Notes Page 4 Example 3: Given : TVK is a right angle Pr ove : 1 is complementary to 2 2 T V 1 X K 1. ngle TVK is a right angle 1. Given 2. ngle 1 is complementary to angle 2 2. y definition of complementary angles Example 4: Given: iagram as shown Prove: angle 1 is supplementary to angle ngle is a straight angle 1. ssumed from the diagram 2. ngle 1 is supplementary to 2. y definition of supplementary angle 2. angles
5 Notes Page notes Monday, September 22, :27 M 2.3 rawing onclusions Example 1: Given : bi sects onclusion :?
6 Notes Page Notes Monday, September 22, :37 M Theorem 4: If angles are supplementary to the same angle then they are congruent. Supp. To the same Theorem 5: If angles are supplementary to congruent angles, then they are congruent Supp. To 's Theorem 6: If angles are complementary to the same angle, then they are congruent. omp. to the same Theorem 7: If angles are complementary to congruent angles, then they are congruent. omp. To 's Example 1: Given: iagram as shown Prove: HFE GFJ H F G E J
7 Notes Page 7 1. EFG and HFJ are straight 1. ssume from diagram angles 2. is supplementary to is supplementary to 3 2. y definition of supplementary angles Supplementary to the same angle
8 Notes Page Notes Monday, September 22, :48 M ddition Property Theorem 8, 9: If a segment(or angle) is added to two congruent segments(or angles), the sums are congruent. E Theorems 9, 10: If congruent segments are added to congruent segments, the sums are congruent. Subtraction Property: Theorem 12: If a segment (or angle) is subtracted from congruent segments (or angles), the differences are congruent. E
9 Notes Page 9 Theorem 13: If congruent segments (or angles) are subtracted from congruent segments (or angles), the differences are congruent. Example 1: Given : Pr ove : Given ddition Property
10 Notes Page Notes Wednesday, September 24, :27 M Multiplication Property: If segments(or angles) are congruent, their like multiples are congruent. Example 1: Given : point s and E are midpo int s of and Pr ove : E E 1. po int s and E are midpo int s of and E 1. Given Multiplication Property ivision Property: If segments(or angles) are congruent, their like divisions are congruent. Example 2: Given : point s and E are midpo int s of and Pr ove : E
11 Notes Page 11 Given : point s and E are midpo int s of and Pr ove : E E 1. po int s and E are midpo int s of and 1. Given 2. E 2. ivision property Example 3: Given : point s and E are midpoint s of and Pr ove : E 1. po int s and E are midpo int s of and 1. Given y definition of midpoint
12 Notes Page 12 Example 4: Given : 1 2 F G bisects E bisects F F Pr ove : 3 4 G E G bisects F E bisects F 1. Given 2. and are straight 2. ssumed from the diagram 3. angles 1 is supplementary to F 2 is supplementary to F 3. y definition of supplementary angles 4. F F 4. Supplementary to congruent angles ivision property
13 Notes Page Notes Thursday, September 25, :19 M Transitive Property: If angles(or segments) are congruent to the same angle(or segment), then they are congruent to each other. If angles (or segments) are congruent to congruent angles(or segments, then they are congruent to each other. Substitution: If angle 1 is complementary to angle 2 and angle 2 is congruent to angle 3, then angle 1 is complementary to angle 3 by substitution Example 1: Given : FG GH KJ KJ K J Pr ove : KG bisec ts FH F G H 1. FG KJ GH KJ 1. Given
14 Notes Page FG GH 2. Transitive Property 3. KG bisects FH 3. y definition of segment bisector
15 Notes Page Notes Thursday, September 25, :50 PM efinition: Two collinear rays that have a common endpoint and extend in different directions are called opposite rays. and are opposit rays. Theorem 18: Vertical angles are congruent. 1 2 Example 1: Given: 2 3 Prove:
16 Notes Page Given Vertical angles 3. Transitive Property
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