Overlapping Triangles Proofs

What is the common side in triangle BDC and CED?

• AB

• EB

• CB

• CD

According to the diagram at the right, which statement is true?

• Triangle DEH is congruent to triangle GFH by AAS

• Triangle DEH is congruent to triangle GFH by SAS

• Triangle DEF is congruent to triangle GFE by AAS

• Triangle DEF is congruent to triangle GFE by SAS

If triangle ABC is congruent KJC, which statement is NOT necessarily true?

• Angle ACB is congruent to angle KJC

• Angle J is congruent to angle B

• JK is congruent to BC

Which CANNOT be used to prove that triangle MNK is congruent to triangle KLM?

• SAS

• ASA

• HL Theorem

Identify any common angles or sides

• JK
• Angle MJK
• LK
• Angle MKJ

Identify common angles or sides

• Angle E
• Angle D
• Angle F
• Angle DGF

The red (ΔKNM) and blue (ΔPLM) triangles are congruent. Identify a common side or angle.

• Angle M
• Angle P
• Angle K
• Angle MLP

The red and blue triangles are congruent. Identify a common side or angle.

• Side DF
• Angle E
• Angle G
• Angle GDE

The red and blue triangles are congruent. Identify a common side or angle.

• Side XY
• Side XZ
• Angle TWZ
• Side YT

Name a pair of overlapping congruent triangles and state how.  (Hint: they have to be overlapping)

• ∆AED ≅ ∆ABC by SAS
• ∆ADB ≅ ∆ACE by SAS
• ∆ADB ≅ ∆ACE by AAS
• ∆ADB ≅ ∆ACE by SSS