Congruence between triangles
17
Which of these three-dimensional figures are congruent? Answer: (a) and (f); (b) and (d); (c)and (e)
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Transcript of Congruence between triangles
- 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