1. Which of these three-dimensional figures are congruent?
Answer: (a) and (f); (b) and (d); (c)and (e)
2. Answer: (a) and (e); (b) and (c); (d)and (f)
3. DEFINITIONS Angles are CONGRUENT if they have the SAME
MEASURE. A B means that mA = mB Ex. If mF = 34 and mG = 34, then F
G Segments are CONGRUENT if they have the SAME LENGTH. AB CD means
that AB = CD Ex. If EF = 2 cm and GH = 2 cm, then EF CD EQUATION is
between NUMBERS or MEASUREMENTS. CONGRUENCE is between GEOMETRIC
FIGURES.
4. We DONT write = between two names of geometric figures
unless: D E C B A BA BAC = DAE AB = BA
5. B C D E FA ABC DEF WHAT ARE THE CORRESPONDING SIDES AND
CORRESPONDING ANGLES?
6. DEFINITION Given a correspondence between two triangles. If
every pair of corresponding angles and corresponding sides are
congruent, then the triangles are congruent.
7. EXERCISES 1. Given that ABE DCF, complete the following
statements by supplying the missing symbols. The correspondence
A___ ___F is a congruence. B CA FE D A D B ____ E ____ AB ____ AE
____ BE ____
8. EXERCISES 2. Given that MQP NQP. List the six pairs of
corresponding, congruent parts of these two triangles. M N P Q
3.For each of the congruences, list the six pairs of corresponding,
congruent parts. a. RQF ABX. You may make a sketch of the triangles
if you wish. b. FHW MRK. Do not use a figure. c. DOG CAT. Do not
use a figure.
9. E BA F C D
10. E BA F C D
11. DEFINITION A side of a triangle is said to be INCLUDED by
the angles whose vertices are the end points of the segment. An
angle of a triangle is said to be INCLUDED by the sides of the
triangle which lie in the sides of the angle.
12. A C B
13. EXERCISES 1. (a) In ABC, which is the included angle of the
sides BC and AB? (b) Which is the included side of A and C? (c)
Which sides include C? (d) Which angles include BC? 2. Consider
GHK. Without drawing a figure, can you discover an easy method of
deciding which sides and angles are included sides and included
angles? (a) Does GH and HK include H? (b) Does G and K include GK?
(c) What is the included angle of GH and GK? (d) What is the
included side of G and H? A C B
