Ch 4 Review Problems pp #7 36, 48,51,52 due MONDAY 12/12
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1 Geometry ongruence Proofs ecember 08, 2016 h 4 Review Problems pp #7 36, 48,51,52 due MONY 12/12 h 5 Review Problems pp #15 50 h 6 Review Problems pp #9 19, Polygons and ongruence ef: polygon is a connected set of at least three line segments in the same plane such that each segment intersects exactly two others, one at each endpoint. The line segments are the sides of the polygon, and the endpoints are its vertices. The number of sides and vertices is always the same, and the polygon is referred to as an n gon if it has n sides and n vertices. ef: Two triangles are congruent iff there is a correspondence between their vertices such that all of their corresponding sides and angles are equal. orollary to the definition of congruent triangles: Two triangles congruent to a third triangle are congruent to each other. 4.3 S and SS ongruence Postulate 5: The S Postulate If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent. Postulate 6: The SS Postulate If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent. 1
2 Geometry ongruence Proofs ecember 08, ongruence Proofs ef: orresponding parts of congruent triangles are equal. E 4.4 ongruence Proofs, cont. 2. Why is =? 3. Why are 1 and 2 right angles? 1 2 Given: is the midpoint of 4. Why is 1= 2? 5. Why is =? 6. Why is? 7. Why is =? 2
3 Geometry ongruence Proofs ecember 08, Why is =? Why is? Given: 1= 2 = 11. Why is =? 13. Why is =? Why is =? Given: = bisects 15. Why is? 16. Why is 1= 2? 17. If 1 and 2 are a linear pair, why is? 3
4 Geometry ongruence Proofs ecember 08, 2016 What is wrong with this proof? Given: bisects and are right angles. Prove: Proof: Statements Reasons 1. bisects Given. 2. = If an angle is bisected, it is divided into two equal angles. 3. = Reflexive. 4. and are right angles Given 5. = ll right angles are equal. 6. S What is wrong with this proof? Given: = Prove: = Proof: Statements Reasons 1. = Given 2. = Reflexive 3. = Reflexive 4. SS 5. = orresponding parts of congruent triangles are congruent 4
5 Geometry ongruence Proofs ecember 08, Isosceles and Equilateral Triangles efinitions: triangle is scalene iff it has no equal sides isosceles iff it has at least two equal sides equilateral iff all of its sides are equal obtuse iff it has an obtuse angle right iff it has a right angle acute iff all of its angles are acute equiangular iff all of its angles are equal Theorem 9: If two sides of a triangle are equal, the angles opposite them are equal. Given: In, = Prove: = Proof: Statements Reasons 1. In, = Given 2. = Reflexive 3. = Given 4. SS 5. = orresponding parts of congruent triangles are equal 5
6 Geometry ongruence Proofs ecember 08, 2016 Theorem 10: If two angles of a triangle are equal, the sides opposite them are equal. orollaries to Theorems 9 and 10: n equilateral triangle is equiangular. n equiangular triangle is equilateral. In, =; =E. 7. What kind of triangle is? E 8. Why is =? 9. What angle do and E have in common? 10. Why is E? 11. Why is = E? 6
7 Geometry ongruence Proofs ecember 08, 2016 T y 48. ST Problem: In this figure, PS is a line segment and PQ=QT=TR=RS. What is the value of y? P Q R S 4.6 SSS ongruence Theorem 11: The SSS Theorem If the three sides of one triangle are equal to the three sides of another triangle, then triangles are congruent. E F 7
8 Geometry ongruence Proofs ecember 08, Why are O and O always equal? 40. What relation does line O have to O? 41. What relation does line O have to O? O In this linkage, the rods can pivot about their ends so the figure can change its shape. 42. Why must lines O and O be the same line? Given: O=O === 43. What does this prove about points O,, and? 8
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Name: Geometry inal am Review. ind the net two numbers in each pattern a.,, 4, 40,,. =, = + 0, = + 0. raw an obtuse angle. M M is the midpoint of M = - M = b. -4,, -6,,,. 6. ind the midpoint of the segment