Proving Congruence – SSS, SAS

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Presentation transcript:

Proving Congruence – SSS, SAS Lesson 4-4 Proving Congruence – SSS, SAS

Ohio Content Standards:

Ohio Content Standards: Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence.

Ohio Content Standards: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.

Ohio Content Standards: Use coordinate geometry to represent and examine the properties of geometric figures.

Ohio Content Standards: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.

Ohio Content Standards: Prove or disprove conjectures and solve problems involving two- and three-dimensional objects represented within a coordinate system.

Ohio Content Standards: Analyze two-dimensional figures in a coordinate plane; e.g., use slope and distance formulas to show that a quadrilateral is a parallelogram.

Ohio Content Standards: Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.

Ohio Content Standards: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.

Ohio Content Standards: Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof.

Side-Side-Side Congruence

Side-Side-Side Congruence If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.

F I G E H

D P V W L M

Side-Angle-Side Congruence

Side-Angle-Side Congruence 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.

Write a proof for the following: S Q T

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.

Assignment: Pgs. 204-206 10-18 evens, 22-25 all, 32-40 all