Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name _________________ Common Core Geometry R A 1) Date ___________________ HW #21 Triangle Proofs B Given: AD ≅ BC E is the midpoint of DC AD DC BC DC Prove: ΔADE ≅ ΔBCE D E Statements 1. AD ≅ BC, E is midpoint of DC. 2. DE ≅ CE 3. AD DE, BC DC 4. ≮D and ≮C are right angles. 5. ≮D ≅ ≮C 6. ΔADE ≅ΔBCD C Reasons 1. Given 2. A midpoint divides a segment into 2 ≅ parts. 3. Given 4. Perpendicular lines form right angles. 5. Right angles are ≅. 6. SAS B 2) A C Given: AC bisects ≮BCD BC ≅ CD Prove: ΔABC ≅ ΔADC D Statements 1. AC bisects ≮BCD. 2. ≮BCA ≅ ≮DCA 3. BC ≅ CD 4. AC ≅ AC 5. ΔABC ≅ ΔADC Reasons 1. Given 2. An angle bisector divides an angle into two congruent parts. 3. Given 4. Reflexive Property 5. SAS OVER 3) D A E C B Statements 1. CD bisects AB. 2. AE ≅ BE Prove: ΔAEC ≅ ΔBED Reasons 1. Given 2. A segment bisector divides the segment into two ≅ parts. 3. Given 4. Vertical angles are ≅. 5. ASA 3. ≮CAE ≅ ≮DBE 4. ≮AEC ≅ ≮BED 5. ΔAEC ≅ ΔBED 4) Given: CD bisects AB ≮CAE ≅ ≮DBE B Given: BD is the perpendicular bisector of AC Prove: ΔABD ≅ ΔCBD A D C Statements Reasons 1. BD is the perpendicular bisector of 1. Given AC. 2. ≮ADB and ≮CDB are right angles. 2. Perpendicular lines form right angles. 3. ≮ADB ≅ ≮CDB 3. Right angles are ≅. 4. AD ≅ CD 4. A bisector divides an angle into 2 ≅ parts. 5. BD ≅ BD 5. Reflexive Property 6. ΔABD ≅ ΔCBD 6. SAS Aim 22: Proving Triangles Congruent by HL, and using Supplementary Angles Do Now: a) If m≮EBC = 110 and m≮BCF = 110, find m≮ABE and m≮DCF. F E b) What do you notice about your answers in (a)? B A C c) What can we conclude about supplements of equal angles? Hypotenuse- Leg Triangle Congruence criteria (HL) : Given two right triangles ABC and A'B'C' with right angles B and B'. If AB = A'B' (leg) and AC = A'C' (hypotenuse), then the triangles are congruent. B B A C A A' C C' B' B' 1. Given: PQ QR, PS Prove: ΔPQR ≅ ΔPSR Statements Q SR, QR ≅ SR R P Reasons S D 2. Given: SM RT, ≮PRM ≅ ≮QTM Prove: ΔSRM ≅ ΔSTM Statements Reasons 3. Given: AB ≅ CD, AB ll CD Prove: ΔABC ≅ ΔDAC Statements Reasons 4. A E Given: ≮ABE ≅ ≮FCD BF || EC C B D Prove: ΔBEC ≅ ΔCFB F Statements Reasons C 5. Given: AB and CD intersect at E. AC ll BD. E is the midpoint of CD. Prove: ΔACE ≅ Δ BDE B E A D Statements Reasons 6. B A D C E Prove: ΔADE ≅ ΔBCE Reasons Statements 7. Given: AE ≅ BE E is the midpoint of DC AD DC BC DC C Given: ≮CBE ≅ ≮DBE A B E AE bisects ≮CAD Prove: ΔACB ≅ ΔADB D Statements Reasons