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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