Page 4: Proving Triangle Congruence

This page demonstrates how to prove triangle congruence using a two-column proof format. It applies the concepts and reasons learned in previous pages to construct a formal proof.

Example: Given: ∠A ≅ ∠D, AE ≅ DC, EB ≅ CB, BA ≅ BD Prove: ΔAEB ≅ ΔDCB

The proof uses reasons such as Given, Vertical Angle Theorem, Third Angle Theorem, and Definition of Congruence to establish that all corresponding parts are congruent.

This example serves as a model for students to follow when working on triangle congruence worksheets with answer keys.

Page 6: Additional Methods for Finding Congruent Sides

This page explores additional methods for finding congruent sides in triangles, including using the distance formula and the Pythagorean theorem.

Example: To find the length of AB when A(3,7) and B(7,4): Use the distance formula: d = √[(x₂-x₁)² + (y₂-y₁)²]

The page also reviews concepts from earlier chapters, such as midpoints and angle bisectors, which can be used to establish congruence in triangles.

Highlight: When two sides of a right triangle are known to be congruent, the unmarked sides must also be congruent due to the Pythagorean theorem.

These concepts are essential for solving more complex congruent triangles worksheets for grade 10 and beyond.

Page 5: Side-Side-Side (SSS) Congruence

This page introduces the Side-Side-Side (SSS) Congruence Postulate, which states that if three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.

Definition: SSS Congruence Postulate: If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

The page emphasizes that not all six corresponding parts need to be congruent for triangles to be congruent. It also introduces the concept of "adding our brain" to the picture, which involves using logical reasoning to identify congruent parts that are not explicitly marked or given.

Example: In some cases, we can use the Reflexive Property to establish that a shared side between two triangles is congruent to itself.

This information is crucial for solving congruent triangles practice problems with SSS answers.

Page 8: Side-Angle-Side (SAS) Congruence

This page introduces the Side-Angle-Side (SAS) Congruence Postulate, which states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Definition: SAS Congruence Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

The page provides examples and asks students to identify what additional information would be needed to prove triangle congruence using the SAS postulate. This approach helps students develop critical thinking skills necessary for solving congruent triangles practice problems with SAS answers.