Proving Angle Relationships

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Presentation transcript:

Proving Angle Relationships Chapter 2.8 Proving Angle Relationships

Concept

Concept

Use the Angle Addition Postulate Prove that the m<1 = 89, if m<2 = 56 and m<JKL = 145. J K 2 1 L

Example 1 Prove that the m1 = 104 if m2 = 58 and mJKL = 162.

Concept

Concept

Example 2 QUILTING The diagram shows one square for a particular quilt pattern. If mBAC = mDAE = 20, and BAE is a right angle, find mCAD. A. 20 B. 30 C. 40 D. 50

Concept

Concept

Concept

Example 3 Proofs Using Congruent Comp. or Suppl. Theorems Given: Prove:

Example 3 Proof: Statements Reasons Proofs Using Congruent Comp. or Suppl. Theorems Proof: Statements Reasons 1. Given 1. m3 + m1 = 180; 1 and 4 form a linear pair. 2. Linear pairs are supplementary. 2. 1 and 4 are supplementary. 3. Definition of supplementary angles 3. 3 and 1 are supplementary. 4. s suppl. to same  are . 4. 3  4

Example 3 In the figure, NYR and RYA form a linear pair, AXY and AXZ form a linear pair, and RYA and AXZ are congruent. Prove that NYR and AXY are congruent.

Example 3 Which choice correctly completes the proof? Proof: Statements Reasons 1. Given 1. NYR and RYA, AXY and AXZ form linear pairs. 2. If two s form a linear pair, then they are suppl. s. 2. NYR and RYA are supplementary. AXY and AXZ are supplementary. 3. Given 3. RYA  AXZ 4. NYR  AXY 4. ____________ ?

Concept

Example 4 Statements Reasons 1. Given 1. 1 and 2 are vertical s. Use Vertical Angles If 1 and 2 are vertical angles and m1 = d – 32 and m2 = 175 – 2d, find m1 and m2. Justify each step. Statements Reasons Proof: 1. 1 and 2 are vertical s. 1. Given

Example 4 A. B. C. D.

Concept

Try it! Pg. 157 #22 - 26