Triangle Congruence
Today you will need:
Grab a warm-up off the wooden desk and get started! :-)
Goals:
Warm-up #1
Better warm-up?
Warm-up #2
Critical Thinking
Of the four transformations you studied in chapter 4, which are rigid motions?
Under a rigid motion, why is the image of a triangle always congruent to the original triangle?
Congruent figures have __________ sides and congruent _______.
Describe the composition of rigid motions
Properties of Triangle Congruence
How can you restate these properties in your own words?
Third Angles Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
Rigid Motions and Congruence
The diagram below is made up of four congruent scalene triangles. For each pair of triangles:
Using corresponding parts...
Using corresponding parts...
Using corresponding parts...
Using corresponding parts...
Using corresponding parts...
Resources
Mod 4 Standards
G.CO.10 Prove and apply theorems about triangles. Theorems include but are not restricted to the following: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motion.
G.CO.11 Prove and apply theorems about parallelograms. Theorems include but are not restricted to the following: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.