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Activity 1 Read each item carefully and choose the correct answer 1. In the figure A YXW = A YZW, which side is congruent to XY? A. YW C. ZY B. XW D. ZW 2. In the same figure, which angle is congruent to ZZ? w A. LX C. ZZYW B. ZY D. ZZWX 3. In the figure ACPA = AALC, which angle is congruent to ZPCA? A . L C. LL B. ZLAC D. ZCPA L.N 4. In the same figure, which side is congruent to PA? A. CP C. LA B. CA D. LC WHAT'S NEW Activity 2 Complete the two-column proof. Choose the correct statement and valid reason in the box below. Given: ZBAD = ZCAD, ZBDA = ZCDA Prove: AB = AC Proof: D Statements Reasons 1. ZBAD = ZCAD, ZBDA = ZCDA 1. 2. AD = AD 2 . 3. AABD = AACD 4. AB = AC Reflexive Property ASA Congruence Postulate Given SAS Congruence Postulate CPCTO Symmetric Property Activity 3 Complete the two-column proof below. Fill in any missing statement or reason and choose your answer in the box. Given OK bisects ZMOT AMOK = A TOK CPCTC Definition of an Angle Bisector Reflexive Property Definition of a Perpendicular Bisecto AMKO = ATOK Given: OK bisects ZMOT; OM = OT Prove: MK = TK Proof: Statements Reasons 1. OM = OT 1. 2. 2. Given 3. 41 = 42 3. 4. OK = OK 4. 5 . 5. SAS Congruence Postulate 6. MK = TK 6. Activity 4 Complete the two-column proof below. A. Given: 2Q = LT; QR = TR Prove: PR = SR Proof: Statements Reasons 1. LQ = LT 1. 2. QR = TR 3. LQRP = LTRS 2 . 4. AQPR = =TSR 4 . 5. PR = SR B. Given: AB = AC; D is the midpoint of BC. Prove: LB = LC Proof: Statements Reasons 1. 1. Given 2. 2. Given 3 . 3. Definition of a midpoint 4 . 4. Reflexive Property 5 . 5. SSS Congruence Postulate 6. CPCTC Activity 5 Complete the two-column proof below. Fill in any missing statement or reason and choose your answer on the box Given Any two right angles are congruent. BD = CD CPCT Definition of an Angle Bisector Reflexive Property AD = AD LBDA and ZCDA are right angles. ABD = AACD B Given: D is the midpoint of BC, BC J. DA at D Prove: AD bisects ZBAC Proof Statements Reasons 1. D is the midpoint of BC 1. 2. 2. Definition of a Midpoint 3. BC _ DA at D 3. 4. 4. Definition of Perpendicular Lines 5. ZBDA = ZCDA 5. 6. 6. Reflexive Property 7. 7. SAS Congruence Postulate 8. ZBAD = CAD 8. 9. AD bisects _BAC 9. Scanned with CamScannerCPCTC 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