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Warm-Up

1. 2. Find m 3. How do you know that a and b are parallel?. ANSWER. 18°. ANSWER. Both are perpendicular to c. Warm-Up. For use after Lesson 4.7 & 4.8. 1. 2. The vertices GHI and RST are G (–2, 5), H (2, 5), I (–2, 2), R (–9, 8), S (–5, 8), and T (–9, 5) .

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Warm-Up

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  1. 1. 2. Find m 3. How do you know that a and b are parallel? ANSWER 18° ANSWER Both are perpendicular to c. Warm-Up For use after Lesson 4.7 & 4.8

  2. 1. 2. The vertices GHI and RST are G(–2, 5), H(2, 5),I(–2, 2), R(–9, 8), S(–5, 8), and T(–9, 5). Is GHI RST? Explain. Is ABC XYZ? Explain. Yes. By the seg. Add. Post.,AC XZ. Also ,AB XY and BC YZ. So ABC XYZby theSSS post. ANSWER Yes.GH = RS = 4, HI = ST = 5, andIG = TR = 3. By the SSS post ., it followsthatGHI RST. Daily Homework Quiz

  3. U Q 10 10 R S T ΔQRS Δ__________

  4. 1. ABE,CBD ANSWER SAS Post. Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem.

  5. 2. FGH,HJK ANSWER HL Thm. Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem.

  6. State a third congruence that would allow you to prove RST XYZ by the SAS Congruence postulate. 3. ST YZ, RS XY ANSWER SY.

  7. BC DA,BC AD ABCCDA ABCCDA STATEMENTS REASONS S BC DA Given Given BC AD BCADAC A Alternate Interior Angles Theorem S ACCA Reflexive Property of Congruence EXAMPLE 1 Use the SAS Congruence Postulate Write a proof. GIVEN PROVE 5. SAS

  8. WYZXZY PROVE Redraw the triangles so they are side by side with corresponding parts in the same position. Mark the given information in the diagram. EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem Write a proof. GIVEN WY XZ,WZ ZY, XY ZY SOLUTION

  9. STATEMENTS REASONS WY XZ Given WZ ZY, XY ZY Given Definition of lines Z andY are right angles Definition of a right triangle WYZand XZY are right triangles. ZY YZ L Reflexive Property of Congruence WYZXZY HL Congruence Theorem EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem

  10. The vertical angles are congruent, so two pairs of angles and a pair of non-included sides are congruent. The triangles are congruent by the AAS Congruence Theorem. EXAMPLE 1 Identify congruent triangles Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use.

  11. There is not enough information to prove the triangles are congruent, because no sides are known to be congruent. Two pairs of angles and their included sides are congruent. The triangles are congruent by the ASA Congruence Postulate. EXAMPLE 1 Identify congruent triangles

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