Geometry Triangle Proof Ideas

What is statement #1?

• BC≅DC

• AC≅EC

• BC≅DC, AC≅EC

• ∆BCA≅∆DCE

What additional information is required in order to know that the triangles are congruent by HL Theorem?

• ∠G ≅ ∠X

• ∠H ≅ ∠V

• GI ≅ XV

• GH ≅ XW

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

• Substitution Property

• Commutative Property

• Reflexive Property

• CPCTC

• Reflective Property

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

• Alternate Exterior Angle are Congruent

• Reflexive Property of Congruence

• Angles that form a linear pair are supplementary.

• Alternate Interior Angles are Congruent.

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

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 ≅ ∠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

AAS congruence theorem

Definition of midpoint

CPCTC

Alternate internal ∠’s are ≅

SM

RM ≅ EM

∠SEM

∠SMR

SAS congruence postulate

△SEM ≅ △KMR

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.

What is the "statement" for step 3 of the proof?

• AH=AN

• AD=AD

• HD=ND

• HD=DN