Triangle-Similarity-Problems

# Triangle-Similarity-Problems - the corollary of the...

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Triangle Similarity Problems Show that PQR and GHJ are similar triangles, and determine JH . Solution: GJ PQ = 15 5 = 3 ; GH QR = 21 7 = 3 . JG PQ = GH QR = 3 , and PQR 2245 JGH (given). PQR JGH by SAS Similarity . By triangle similarity, JH PR = GJ QP . JH 4 = 15 5 = 3 . JH = 12 . Note that the statement " PQR JGH " is true, but the statement " PQR GHJ " is false . ? 21 15 7 5 4 R H J G Q P Problem 1: Given PQR and GHJ as shown such that Q 2245 G :

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To Prove: 1) APQ ABC and 2) PQ BC . Triangle Similarity Problems AP AB = 3 4 = AQ AC and PAQ 2245 BAC because PAQ = BAC . 1) APQ ABC by SAS Similarity . 2) To prove that PQ BC , we could directly apply the converse of the Basic Proportionality Theorem. However, using the concept similarity, we prove these lines are parallel using
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Unformatted text preview: the corollary of the Alternate Interior Angles Theorem called the "Congurent Corresponding Angles" Theorem: Now, ∠ APQ and ∠ ABC are corresponding angles form by AB as a transversal of PQ and BC . Since APQ ∼ ABC , ∠ APQ 2245 ∠ ABC by triangle similarity . ∴ PQ BC by Corollary 3.4.3 , the "Congruent Corresponding Angles" Theorem. Q E D (3/4) s (3/4) r s r Proof: [ From the original figure, visualize the two overlapping triangles separately.] Problem 2: On ABC, points P and Q are points such that i) A - P - B and A - Q - C ii) AP = (3/4) AB and AQ = (3/4) AC . P Q A C A Q P Q A B C C B A P B...
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Triangle-Similarity-Problems - the corollary of the...

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