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Direction: Use the definitions, theorems, Triangle Congruence Postulates, and CPCTC to solve the problem below. Explain your answer and refer to the rubric that follow. The map below shows four different cities and a town. Assuming that Bogo City is exactly halfway between two pairs of cities and town: it is halfway between Cebu City and Lapu-Lapu City and halfway between Talisay City and Cordova Using the information in the map, what is the distance between Cebu City and Talisay City? Cordova Cebu City Bogo City 16 km 14 km Lapu-Lapu City 8 km Talisay CityCPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent. It means that once the two triangles are proven to be congruent, then the three pairs of corresponding sides must be congruent, and three pairs of corresponding angles must also be congruent. So, if AMAT = AGEO, then all the corresponding sides and angles of the triangles are congruent. M G A E This means that the pairs of angles and sides are congruent since AMATE AGEO. ZM = LG MA = GE LA = LE AT = EO LT = LO MT = GO To prove that the corresponding parts of two triangles are congruent, we need to prove first that the two triangles are congruent. After that, it will follow that the remaining corresponding parts of the two congruent triangles are congruent by CPCTC. CPCTC is usually used at the end of a proof to show that two angles or two sides are congruent. Example 1: Given: CL = AP , 41 = 42 Prove: LA = PC Proof: A Statements Reasons 1. CL = AP 1. Given 2. 41 = 42 2. Given 3. CA = AC 3. Reflexive Property 4. ACAL = ACP 4. SAS Congruence Postulate 5. LA = PC 5. CPCTC Example 2: B Given: BC = DA, BC |! DA Prove: LB = LD Proof: A D Statements Reasons 1. BC = DA, BC || DA 1. Given 2. LBCA = LDAC 2. Alternate interior angles of parallel lines cut by a transversal are congruent. 3. CA = AC 3. Reflexive Property 4. ABCA = A DAC 4. SAS Congruence Postulate 5. LB= LD 5. CPCTC Example 3: Given: LBDA = ZCDA, AD bisects ZBAC. Prove: LB = LC Proof: B D Statements Reasons 1. ZBDA = ZCDA 1. Given 2. AD = AD 2. Reflexive Property 3. AD bisects _BAC 3. Given 4. LBAC = LCAD 4. Definition of an Angle Bisector 5. ABAD = ACAD 5. ASA Congruence Postulate 6. ZB = LC 6. CPCTC Scanned with CamScanner