Do Now Find the value of x that will make a parallel to b. (7x – 8)° 62° a b (44 – 3x)° a b 25° 7x – 8 + 62 = 180 7x + 54 = 180 7x = 126 x = 18 44 – 3x + 25 = 180 69 – 3x = 180 -3x = 111 x = -37
Prove Basic Geometry Proofs by Direct Proofs A proof is a logical argument that establishes the truth of a statement. Developing Proofs: Make sure each step in the argument is in proper chronological order in relation to earlier steps. Make sure that your argument is clearly developed and that each step is supported by a property, theorem, postulate or definition.
Proving Lines Are Parallel To prove that two coplanar lines that are cut by a transversal are parallel, prove that any one of the following statements is true: A pair of alternate interior angles are congruent. A pair of corresponding angles are congruent. A pair of interior angles on the same side of the transversal are supplementary.
2) Given: 4 & 5 are supplementary. Prove: g||h Statements Reasons 1) Given: 1 2 Prove: m||n 1 2 2 3 1 3 m ||n Given Vertical Angles Theorem Transitive Property of Congruence Corresponding Angles Converse 1 2 3 m n Statements Reasons 2) Given: 4 & 5 are supplementary. Prove: g||h 4 & 5 are supplementary 5 & 6 are supplementary 4 6 g||h Given Linear Pair Postulate Congruent Supplements Theorem Alternate Interior Angles Converse h g 4 6 5
3) Given: m1 = 53 m 2 = 127 Prove: j||k Statements Reasons 1 3 2 j 3 1 j||k Given Linear Pair Postulate Substitution Property of Equality Subtraction Property Substitution Definition of Congruent Angles Corresponding Angles Converse
Proving Lines Are Perpendicular To prove that two intersecting lines or line segments are perpendicular, prove that one of the following is true: When the two lines or line segments intersect, they form right angles. When the two lines or line segments intersect, the form congruent adjacent angles.
Given: 1 2, 1 & 2 are a linear pair. Prove: g h Statements Reasons 1 2 1 = 2 1 and 2 are a linear pair 1 & 2 are supplementary m1 + m2 = 180 m1 + m 1 = 180 2(m 1) = 180 m 1 = 90 1 is a right angle g h Given Definition of congruent angles Linear Pair Postulate Definition of Supplementary Angles Substitution Property of Equality Distributive Property Division Property of Equality Definition of a Right Angle Definition of Perpendicular Lines