Unit 1 Lesson 13 Proving Theorems involving parallel and perp lines WITH ANSWERS!.notebook. Proofs involving Parallel lines

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1 Unit 1 Lesson 13 Proofs involving Parallel lines We will need to recall the different postulates and Theorems involving Parallel lines... Can you name the following types of angles from the diagram below??? and 11 3 and 6 1 and 9 7 and 9 2 and 8 Oct 6 7:46 AM 1

2 Given Corresponding angles are Vertical angles are when the lines are II Transitive Property of Oct 3 1:07 PM 2

3 note: You may not use the theorem you are trying to prove as part of your "Reasons" Oct 3 1:08 PM 3

4 Prove: The Same Side-Exterior Angle Theorem Given: a b Prove: 1 and 3 are Supplementary Statements Reasons Oct 3 1:09 PM 4

5 Given: m<3= 85 o m<4 = 85 o r Prove: r s 3 4 s Statements Reasons m<3 = 85 o, m< 4 = 85 o Given m<3 = m<4 <3 <4 = implies when 2 angles are = to 85 0 they are equal in measure. 9. r ll s when alternate exterior angles are the lines are II. 9. Oct 3 1:10 PM 5

6 Given: Prove: <2 and <4 are r supplementary s Statement Reason <2 and <4 are given supplementary <4 <5 vertical angles are m<4=m<5 implies = m<1+m<4 = 180 m<2+m<5 = 180 <2 & <5 are supplementary r II s Sumplementary angles sum is substitution property If 2 angles sum is 180, they are supplementary. when same side interior angles are supplementary, the lines are II s r Oct 3 1:11 PM 6

7 Given: Prove: n k m n m k k n 1 m 2 3 Statement n k <1 <2 m n <2 <3 <1 <3 m k Reason Given corresponding angles are Given corresponding angles are Transitive property of congruency when corresponding angles are, the lines are II when lines are II when lines are II Oct 3 1:12 PM 7

8 Statements Reasons 1) A 1 2 B D 3 4 C Given: AB ll DC, <1 <2 AB ll DC, <1 <2 2) <2 <4 1) Given 2) corresponding angles are when lines are II 3) <4 <1 3) Transitive Property 4) <1 <3 4) corresponding angles are when lines are II 5) <4 <3 5) Transitive Property Prove: <3 <4 Oct 3 1:12 PM 8

9 Given: l ll m, n ll k Prove: <1 <5 Statements Reasons 1) l ll m, n ll k 1) Given n k 1 m l 4 2) <1 <3 2) corresponding angles <3 <5 3) <1 <5 are when lines are II 3) Transitive Property Oct 3 1:12 PM 9

10 n k 1 m l 4 Given: <3 <4, m ll l Prove: <2 <4 Statements 1) <3 <4, m ll l 1) given Reasons 2) n II k 2) when alternate interior angles are, the lines are II 3) <2 <3 3) when line are parallel, alternate interior angles are. 4) <2 <4 4) Transitive Property of Oct 3 1:12 PM 10

11 c Proof...that the sum of the interior angles of a triangle add up to 180 o a statements reasons 4 5 b 1) Draw line a, parallel to line b... so a b 1) Through any point, there exists a line parallel to a given line 2) m<1=m<4 2) alternate interior angles are = in measure when the lines are parallel 3) m<5=m<3 3) same as reason 2 0 4) m<1+m<2+m<3=180 4) a straight angles measure ) m<4+m<2+m<5= ) substitution property Oct 3 1:21 PM 11

12 Given: <1 is an exterior angle B Prove: m<1 = m<a + m<b 2 1 A C Statements <1 is an exterior angle <1&<2 are a linear pair <1& <2 are supplementary m<1 + m<2 = 180 o m<2 +m<b +m<a = 180 o m<1 + m<2 = m<2 +m<a + m<b m<1 = m<a + m<b Reasons given 2 angles that share a common vertex and whose noncommon sides are opposite rays, form a linear pair. If 2 angles form a linear pair, then they are supplementary. Supplementary angles add up to 180 degrees. The 3 angles of any triangle sum to 180 degrees. Substitution Property Subtraction property of equality. Oct 6 12:57 PM 12

13 Homework Unit 1 Lesson 13 found on the website Oct 6 1:05 PM 13