Day 3: Triangle Congruence

by

Richard Moushegian


Objective: To identify congruent triangles and right triangles using basic congruence postulates and theorems.

GA QCC: #16


Lesson: Triangle Congruence (Definition)

NAME: _______________________

1. By definition, 2 triangles are congruent if and only if the corresponding angles are congruent and the corresponding sides are congruent.

2. Why do we say "if and only if"? Because if the 2 triangles are congruent, then we know the corresponding angles and sides are congruent. ALSO, if the corresponding angles and sides are congruent, then we know the 2 triangles are congruent. So, the definition works in both directions.

3. If 2 triangles, ABC and DEF, are congruent, then angle A is congruent to angle D; angle B is congruent to angle E; etc. Do you think side AB is congruent to side DE? ___________________

Why? _____________________________________________________________

4. Click HERE (Figure 1) for an example of 2 congruent triangles. Answer the following questions:

4a. Are angles A and D congruent? ________________

4b. Are angles B and E congruent? ________________

4c. Are angles C and F congruent? _________________

Do we need to measure them? _____________________

Why?_________________________________________

4d. Is side AB congruent to side DE? _______________

(Measure them!)

4e. Is side BC congruent to side EF?________________

(Measure them.)

4f. Is side CA congruent to side FD?________________

4g. If we know all 3 corresponding angles are congruent and two of the corresponding sides are congruent, do you think we need to measure the third sides?__________________________

WHY? (Hint: Discuss the shape of the triangles.)_______________

_______________________________________________________


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