Practice and SAS Postulate

This page provides a practice problem for the SSS postulate and introduces the Side-Angle-Side (SAS) Postulate.

The practice problem reinforces the application of the SSS postulate:

Example: Given: EG = GH, EF = HF, and F is the midpoint of GI. Prove: Triangle EFG is congruent to Triangle HFG.

The solution demonstrates how to use given information and the definition of a midpoint to prove triangle congruence using the SSS postulate.

The page then introduces the SAS postulate:

Definition: The SAS postulate 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 two triangles are congruent.

This definition is crucial for understanding another method of proving triangle congruence, expanding students' toolkit for geometric proofs.

Highlight: The SAS postulate requires that the angle be included between the two congruent sides, which is a key distinction from the SSS postulate.

Applying SAS Postulate

This page focuses on applying the Side-Angle-Side (SAS) Postulate through various examples and practice problems. It emphasizes the importance of identifying the correct information needed to prove triangle congruence using SAS.

The first example asks what additional information is needed to prove triangle DEF congruent to triangle DGF using SAS:

Example: Given: EF = GD and DF = FD (reflexive property). The solution explains that the angle EFD or DFG is needed, as it's the angle between the two known congruent sides.

Another example explores what's needed to prove triangle LBE congruent to triangle BNL using SAS:

Example: Given: Angle ELB = Angle BNL and LB = BL (reflexive property). The solution indicates that LE = NL is the additional information needed.

These examples help students understand the specific requirements of the SAS postulate and how to identify missing information in congruence proofs.

Highlight: When using the SAS postulate, it's crucial to ensure that the known angle is included between the two congruent sides.

The page also includes practice problems that ask students to determine whether SSS or SAS can be used to prove triangle congruence, or if there's not enough information provided.

Identifying Congruent Triangles

This final page focuses on identifying when to use the SSS or SAS postulates to prove triangle congruence. It presents several scenarios and asks students to determine which postulate, if any, can be used to prove congruence.

Example: One problem shows two triangles with three pairs of congruent sides marked. The solution explains that SSS can be used to prove these triangles congruent.

Example: Another problem presents two triangles with two congruent sides and one congruent angle marked. The solution points out that SAS cannot be used because the given angle is not included between the congruent sides.

These examples help students distinguish between situations where SSS, SAS, or neither postulate can be applied.

Highlight: It's important to carefully examine the given information and the position of congruent parts when deciding which postulate to use.

The page concludes with a "Got It!" section, reinforcing the concepts learned throughout the lesson.

Vocabulary: Reflexive property is often used in these proofs, stating that a side is congruent to itself.

This comprehensive review of SSS and SAS postulates provides students with the tools to prove triangle congruence in various scenarios, enhancing their understanding of geometric proofs.

Triangle Congruence by SSS & SAS

This page introduces the Side-Side-Side (SSS) Postulate for proving triangle congruence. The SSS postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

Definition: The SSS postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

An example is provided to demonstrate how to use the SSS postulate to prove triangle congruence:

Example: Given: LM = NP, LP = NM, and LN is congruent to itself (reflexive property). Prove: Triangle LMN is congruent to Triangle NPL.

The page also includes a "Got It?" section with another example:

Example: Given: BC = BF, CD = FD, and BD is congruent to itself (reflexive property). Prove: Triangle ABC is congruent to Triangle BFD.

These examples help students understand how to apply the SSS postulate in different scenarios, reinforcing the concept of proving triangles congruent using SSS.