Geometry Triangles Proofs

In the given proof, what is the reason for step 1?

• Angles that form a linear pair are supplementary.

• Angles of Equal Measure are Congruent

• Reflexive Property of Congruence

• Definition of a Perpendicular Bisector

In the given proof, what is the statement for step 2?

Why are these 2 triangles congruent, based on your proof?

• ASA

• SAS

• SSS

• Hypotenuse Leg Thm

Since segment BD is part of both triangles, it is congruent to itself, what do we call this?

• Substitution

• Commutative

• Reflexive

• CPCTC

Statements Reasons

• ∠1 ≅ ∠2

• JG bisects EH at F

• EF ≅ FH

• ∠3 ≅ ∠4

• △EFJ ≅ △HFG

• ∠EJF ≅ ∠HGF

• EJ ≅ GH

• JF ≅ FG

• Definition of bisect

• Definition of midpoint

Fill in the proof with the labels below.

f

g

h

b

c

e

i

a

d

j

Alternate internal ∠’s are ≅

SAS congruence postulate

Definition of midpoint

SM

∠SEM

AAS congruence theorem

△SEM ≅ △KMR

CPCTC

RM ≅ EM

∠SMR

Given: \overline{PQ}\cong\overline{ST},\ \angle PQS\cong\angle RSQ Prove: \Delta PQS\cong\Delta RSQ

• Given

• Reflexive Property

• SAS Congruence Postulate

• SSA Congruence Postulate

• SSS Congruence Postulate

• Symmetric Property

• Alternate Interior Angle Thm.

Statements Reasons

1. ∠A ≅ ∠C 1. ​ (a)  

2. BD bisects ∠ABC 2. ​ (b)  

3. ∠DBA ≅ ∠DBC 3. ​ (c)  

4. BD ≅ BD 4. ​ (d)  

5. △ABD ≅ △CBD 5. ​ (e)  

• Given

• Definition of bisect

• Reflexive

• AAS

• Definition of midpoint

• SSS

• SAS

• ASA

• Vertical Angles Theorem

• Linear Pairs Theorem

Statements Reasons

1. ​ (a)   1. Given

2. ​ (b)   2. Given

3. ​ (c)   3. Definition of bisect

4. ​ (d)   4. Vertical Angles Theorem

5. ​ (e)   5. ASA

• ∠1 ≅ ∠2

• JG bisects EH at F

• EF ≅ FH

• ∠3 ≅ ∠4

• △EFJ ≅ △HFG

• ∠EJF ≅ ∠HGF

• EJ ≅ GH

• JF ≅ FG

• Definition of bisect

• Definition of midpoint

Statements Reasons

• ∠DBM ≅ ∠FCM

• ∠BDM ≅ ∠CFM

• M is the midpoint of DF

• DM ≅ MF

• △BDM ≅ △CFM

• ∠BMD ≅ ∠CMF

• BM ≅ CM

• BD ≅ CF

• Definition of midpoint

• Definition of bisect