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Fired Up about Section 7.2 Two Proof Oriented Triangle Theorems Richuan Hu Section 8 Honors Geometry Mr. Pricci
Now douse it and learn • As the section name implies, there is two theorems that are often used in proofs about triangles in this section. • The two theorems are the No – Choice Theoremand the AAS Theorem.
The No Choice theorem states that… • If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent. C 3 A 1 2 B
Do You have A Choice? • No, you don’t, suck it up, you’ll live. • Because if two angles of two triangles are the same, no matter how the sides differ, the third angle is going to be the same.
Proof that you don’t have a choice • It is a truth universally acknowledged, that any triangle big or small always has a sum of 180 degrees. • If 1 A, 2 B • By subtraction, angle 3 and angle C must be congruent 3 C 1 B A 2
Exemplifying your lack of choice Since the two triangles are right triangles, the right angles are congruent. Because the big triangle is isosceles as given, the 70 degree angle is congruent to the corresponding one on the other side. Therefore, angle 3 is congruent to the adjacent angle by no choice. Angle 3 is 20 degrees from 180 – 90 – 70. • Pg 321 #11)Find m 3in diagram as marked. 3 70 ° C R Pg 303 Sample Problems #1 Given: R C Prove: H U I H U
Answers • Pg 303 #1 S R • R C • ABE DBC • H U • Given • Vertical angles are congruent • No Choice Theorem
The AAS StAteS that… • If there exist a correspondence between the vertices of two triangles such that two angles and a nonincluded side of one are congruent to the corresponding parts of the other, then the triangles are congruent. • In English If two angles and a side not in between them of two triangles are congruent, the two triangles are congruent.
Proof of AAS S R • C F • A E • B E • ABC DEF • Given • Given • No Choice Theorem • ASA (1,2,3) Givens:
The AAS is usually associated with… • Theorems that prove triangles congruent, like the SSS, ASA, and SAS.
Works Cited • Geometry for Enjoyment and Challenge, McDougal & Company, Evanston, Illinois, 1997. • Austen, Jane. Pride and Prejudice, Penguin Books, New York,2006. • http://www.mathwarehouse.com/geometry/congruent_triangles/angle-angle-side-postulate.php