Congruence between triangles
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- 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