Geometry: Independent Triangles

Match the following items. Given: TQ bisects RTS R ≅ S Prove: TQ ⊥ RS 1. Segment TQ bisects ∠RTS; ∠R ≅ ∠S 2. ∠1 ≅ ∠2 3. TQ ≅ TQ 4. Triangle RTQ congruent to Triangle STQ 5. ∠3 ≅ ∠4 6. Segment TQ ⊥ Segment RS

1. Given 2. Definition of angle bisector. 3. Reflexive 4. AAS 5. CPCTE 6. Definition of perpendicular.

Match the following items. Given: 1 = 2 3 = 4 D midpoint of BE BC = DE Prove: ∠A = ∠E 1. ∠1=∠2, ∠3=∠4, D is midpoint of segment BE, BC = DE 2. BD = DE 3. BC = BD 4. Triangle ABD congruent to Triangle EBC 5. ∠A = ∠E

1. Given 2. Definition of midpoint 3. Substitution 4. ASA 5. CPCTE

Match the reasons with the statements in the proof to prove that BC = EF, given that triangles ABC and DEF are right triangles by definition, AB = DE, and A = D. Given: ABC and DEF are right triangles AB = DE A = D Prove: BC = EF 1. ABC and DEF are right triangles, AB = DE, A = D 2. ABC ≅ DEF 3. BC = EF

1. Given 2. LA 3. CPCTE

Match the following items. Given: 2 = 3 4 = 5 Prove:RS = RT 1.∠2 = ∠3, ∠4=∠5 2.∠1 = ∠3 3.∠1 = ∠2 4.VR=VR 5.Triangle VSR congruent to Triangle VTR 6. RS = RT

1. Given 2. Vertical angles are equal. 3. Substitution 4. Reflexive 5. ASA 6. CPCTE

Which of the following are used to prove that triangles are congruent?

ASA SSS AAS SAS

Complete the following proof related to the figure below. Given: A, B are rt 's AC = BD Prove:MC = MD Which of the following could not be used as the reason in line 3 of the proof?

HL

Complete the following proof related to the figure below. Given: TQ bisects RS RT = ST Prove: TQ ⊥ RS Which of the following would be the reason for line 4 in the proof?

SSS

Given: A, B are rt 'sAC = BD Prove:MC = MD Which of the following statements is the reason for line 2 in the proof?

Vertical angles are equal.

Complete the following proof related to the figure below. Given: TQ is the perpendicular bisector of RS Prove:∠R = ∠S Which of the following could be statements in line 2 in the proof? Select all that apply.

∠3=∠4 RQ=SQ