Geometry Chapter 4 Review for Pearson enVision Common Core 2018 (Topic 4: Triangle Congruence)

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This video serves as a a compilation design to prepare students for a test on Topic 4: Triangle Congruence in the Pearson enVision Geometry Common Core 2018 curriculum.

Topics included in this video are....

4-1: Congruence:
Congruence refers to the state of two or more geometric figures having the same size and shape. When two figures are congruent, their corresponding sides and angles are equal. Congruence is a fundamental concept in geometry and is often used to establish relationships, make comparisons, and prove the equality of figures.

4-2: Isosceles and Equilateral Triangles:
Isosceles triangles are triangles that have two sides of equal length. The angles opposite the equal sides are also congruent. Equilateral triangles are a special type of isosceles triangle where all three sides are equal in length. Equilateral triangles have all angles measuring 60 degrees.

4-3: Proving and Applying the SAS and SSS Congruence Criteria:
SAS (Side-Angle-Side) and SSS (Side-Side-Side) are congruence criteria used to prove that two triangles are congruent. SAS states that if two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle, then the triangles are congruent. SSS states that if the three sides of one triangle are congruent to the corresponding three sides of another triangle, then the triangles are congruent.

4-4: Proving and Applying the ASA and AAS Congruence Criteria:
ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side) are congruence criteria used to prove triangle congruence. ASA states that if two angles and the included side of one triangle are congruent to the corresponding two angles and included side of another triangle, then the triangles are congruent. AAS states that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the triangles are congruent.

4-5: Congruence in Right Triangles:
Congruence in right triangles involves specific criteria for proving the congruence of right triangles. These include the Hypotenuse-Leg (HL) criterion, which states that if the hypotenuse and one leg of one right triangle are congruent to the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent.

4-6: Congruence in Overlapping Triangles:
Congruence in overlapping triangles refers to the concept of proving the congruence of two triangles that share a common side or angle. This involves establishing the congruence of corresponding parts, such as sides and angles, in order to show that the two triangles are congruent.

Understanding congruence and the various criteria for proving triangle congruence is essential in geometry. It allows for the analysis of relationships between figures, the identification of congruent parts, and the ability to make accurate comparisons and deductions.

These videos are designed to review and reteach high school Geometry content. My videos cover…

Points, Lines, and Planes,
Angles and Angle Relationships,
Triangles,
Quadrilaterals,
Circles,
Similarity and Proportions,
Congruent Figures,
Coordinate Geometry,
Transformations,
Area and Perimeter,
Volume and Surface Area,
Right Triangles and Trigonometry,
Geometric Proofs,
Constructions,
Non-Euclidean Geometries.

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa
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