Math 2 Geometry Based on Elementary Geometry, 3 rd ed, by Alexander & Koeberlein 3.2 Corresponding Parts of Congruent Triangles.

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Presentation transcript:

Math 2 Geometry Based on Elementary Geometry, 3 rd ed, by Alexander & Koeberlein 3.2 Corresponding Parts of Congruent Triangles

CPCTC Corresponding parts of congruent triangles are congruent. We first need to prove two triangles are  Could possibly use SSS, SAS, ASA, AAS A B C D E F

Example #1 Given: Ray WZ bisects  TWV Seg WT  Seg WV Prove: Seg TZ  Seg VZ T Z V W

Example #1a Given: Ray WZ bisects  TWV Seg WT  Seg WV Prove: Seg WZ bisects Seg TV T Z V W

Three types of  conclusions Proving triangles congruent Proving the congruence of corresponding parts of triangles. First need to prove the triangles are congruent. Establishing further relationships like in previous example. Need to first establish two triangles are congruent.

Example 2 Given: Seg ZW  Seg YX Seg ZY  Seg WX Prove: Seg ZY || Seg WX 2 ZY X W 1

Right Triangles Hypotenuse Leg

HL (Hypotenuse-Leg) Theorem Method for Proving Triangles Congruent If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of a second triangle, then the triangles are congruent. Hypotenuse Leg

Example a.SegAB  SegEC and SegAC  Seg ED b.  A   E and C is midpoint of SegBD c.SegBC  SegCD and  1   2 d.SegAB  SegEC and SegEC bisects SegBD B A CD E 12

Example a.SegAB  SegEC and SegAC  Seg ED b.  A   E and C is midpoint of SegBD c.SegBC  SegCD and  1   2 d.SegAB  SegEC and SegEC bisects SegBD B A CD E 12

Example Cite reason why rt  ABC  rt  ECD a.SegAB  SegEC and SegAC  Seg ED B A CD E 12

Example a.SegAB  SegEC and SegAC  Seg ED b.  A   E and C is midpoint of SegBD B A CD E 12

Example a.SegAB  SegEC and SegAC  Seg ED b.  A   E and C is midpoint of SegBD c.SegBC  SegCD and  1   2 B A CD E 12

Example a.SegAB  SegEC and SegAC  Seg ED b.  A   E and C is midpoint of SegBD c.SegBC  SegCD and  1   2 d.SegAB  SegEC and SegEC bisects SegBD B A CD E 12

Pythagorean Theorem The square of the length (c) of the hypotenuse of a right triangle equals the sum of the square of the lengths (a and b) of the legs of the triangle: c b a

Square Roots Property Let x represent the length of a line segment, and let p represent a positive number. Then, Note: Different from Square Roots Property in Algebra…

Example Find the length of the third side of the  a.Find c if a = 6 and b = 8. c b a

Example Find the length of the third side of the  a.Find c if a = 6 and b = 8. b.Find b if a = 7 and c = 10 c b a