# Triangles and Types of triangles&Congruent Triangles (Congruency Rule)

21 de Sep de 2017
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### Triangles and Types of triangles&Congruent Triangles (Congruency Rule)

• 6. Types of Triangles  Equilateral triangle: A triangle with three congruent (equal) sides and three equal angles. These marks indicate equality.
• 7. Types of Triangles  Isosceles triangle: A triangle with at least two congruent (equal) sides.
• 8. Types of Triangles  Scalene triangle: A triangle that has no congruent (equal) sides.
• 9.  Acute Angled Triangles: Has all angles more than (0 degree) and less than (90 degree). Types of Triangles
• 10. Types of Triangles  Right triangle: Has only one right angle (90 degrees). This box indicates a right angle or a 90-degree angle.
• 11.  Obtuse Angled Triangles: Has one angles more than (90 degree) and less than (180 degree). Types of Triangles One angle greater than 90 And less than 180 degree
• 13. Congruence triangles are triangles that have the same shape and the same size. A C B D F E ABC  DEF When we say that triangles are congruent there are several repercussions that come from it. A  D B  E C  F AB DE BC EF AC DF
• 14. 1. SSS Congruency Theorem  3 pairs of congruent sides Six of those statements are true as a result of the congruency of the two triangles. However, if we need to prove that a pair of triangles are congruent, how many of those statements do we need? Because we are working with triangles and the measure of the angles and sides are dependent on each other. We do not need all six. There are three special combinations that we can use to prove congruency of triangles. 2. SAS Congruency Theorem  2 pairs of congruent sides and congruent angles between them 3. ASA Congruency Theorem  2 pairs of congruent angles and a pair of congruent sides
• 15. 1. SSS Congruency Theorem  3 pairs of congruent sidesA B C 5 12 ABC  DFE D FE 5 12 5 DFmABm 12 FEmBCm 13 DEmACm
• 16. 2. SAS Congruency Theorem  2 pairs of congruent sides and congruent angles between them G H I L J K 7 70 70 mH = mK = 70° GHI  LKJ 7 5 LKmGHm 7 KLmHIm
• 17. The SAS Congruency Theorem does not work unless the congruent angles fall between the congruent sides. For example, if we have the situation that is shown in the diagram below, we cannot state that the triangles are congruent. We do not have the information that we need. G H I7 50 Angles I and J do not fall in between sides GH and HI and sides LK and KJ respectively. L J K 50 7
• 18. 3. ASA Congruency Theorem  2 pairs of congruent angles and one pair of congruent sides. M N O 70 50 mN = mR mO = mP MNO  QRP Q R P 7050 7 RPmNOm 77