Page 2: Triangle Congruence Crossword #2

This page continues with two more triangle congruence proofs, focusing on the AAS (Angle-Angle-Side) and ASA (Angle-Side-Angle) congruence theorems.

The first proof involves triangles ABD and CBD, with the given information:

• ∠A = ∠C
• BD bisects ∠ABC

Definition: An angle bisector is a line that divides an angle into two equal parts.

The proof uses the AAS congruence theorem to establish that ΔABD ≅ ΔCBD.

The second proof deals with triangles CME and KMN, given:

• NR || CE
• M is the midpoint of CR

This proof employs the ASA congruence theorem to show that ΔCME ≅ ΔKMN.

Example: The proof uses the concept of vertical angles, which are always congruent. In this case, ∠CME ≅ ∠KMN because they are vertical angles.

The crosswords with congruent triangle proofs pdf format continues to engage students in actively thinking about each step of the proof process.

Page 3: CPCTC Crossword

The final page introduces the concept of CPCTC (Corresponding Parts of Congruent Triangles are Congruent) in triangle congruence proofs.

The first proof involves triangles LMO and NMO, with the given information:

• LM = NM
• MO bisects ∠LMN

The proof uses the SAS congruence theorem to establish triangle congruence, then applies CPCTC to prove that O is the midpoint of LN.

Highlight: CPCTC is a powerful tool in geometry proofs, allowing us to conclude that corresponding parts of congruent triangles are also congruent.

The second proof deals with triangles ACB and ECD, given:

• AB || ED
• C is the midpoint of AE

This proof employs the AAS congruence theorem and CPCTC to show that BC = DC.

Quote: "Corresponding Parts of Congruent Triangles are Congruent (CPCTC)"

The crossword puzzle format continues to reinforce the understanding of triangle congruence proofs while introducing the important concept of CPCTC.