1. Geometry SOL review Session 2

2. Triangle relationships Congruent triangles Similar triangles Right triangles Triangle inequalities

3. Classifying Triangles Their angles Acute Right Obtuse Equiangular Their sides Scalene Isosceles Equilateral

4. More triangle theorems The sum of the interior angles in a triangle is 180˚. There can be at most one right or obtuse angle in a triangle. Acute angles in a right triangle are complementary. The measure of the exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

5. Isosceles Triangles An isosceles triangle is a triangle with two congruent sides. The congruent sides are called legs and the third side is called the base.

6. Isosceles Triangles If two sides of a triangle are congruent, then the angles opposite those sides are congruent. If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

7. Special segments in triangles There are special segments associated with triangles: Medians, Altitudes, and Perpendicular Bisectors

8. Special segments in triangles The perpendicular bisector can pass through a vertex in an isosceles triangle (and therefore in an equilateral triangle).

9. Congruent Triangles SSS side, side, side SAS side, included angle, side ASA angle, included side, angle AAS angle, angle, side HL hypotenuse, leg Match with the letter

10. Congruent Triangles

12. Similar Triangles AA Angle, angle If 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar. SSS Side, side, side If the measures of the corresponding sides of 2 triangles are proportional, then the triangles are similar. SAS Side, angle, side If the measures of 2 sides of a triangle are proportional to the measures of 2 corresponding sides of another triangle and the angles between them are congruent, then the triangles are similar.

13. Similar Triangles 1.DE║GF Prove ΔDEC~ ΔFGC 2. 3. G and H are midpoints of DE and EF. Prove ΔDEC~ ΔGEH

14. Right Triangles-Pythagorean theorem Given any Right Triangle, A 2 + B 2 = C 2 C A B Let A = 3 and B = 4 C 2 = A 2 + B 2 C 2 = 3 2 + 4 2 C 2 = 9 + 16 C = 5 You should memorize some Pythagorean triples

15. More Pythagorean Theorem If A 2 + B 2 > C 2, you have an acute triangle. Remember you can just try 2 for all sides to remember how the inequality goes 4 + 4 > 4 If A 2 + B 2 < C 2, you have an obtuse triangle. 16+ 25 < 81 4 5 9 2 2 2

16. Special Right Triangles 45-45-90 30-60-90 x 2x 60˚ 30˚ x x 45˚ 60˚ 7 b a

17. Special Right Triangles 45-45-90 30-60-90 x 2x 60˚ 30˚ x x 45˚ 7 b a

18. Right Triangle Trigonometry Tan. = Opp. Adj. Cos. = Hyp. Adj. S in. = Hyp. Opp. Hyp. Adj. Opp. Tan. = Opp. Adj. Cos. = Hyp. Adj. Sin. = Hyp. Opp. Hyp. Adj. Opp. Angle of Perspective

19. Right Triangle Trigonometry Find x x 12 25˚

20. Triangle inequalities The smallest angle is across from the smallest side. List angles from smallest to largest The largest angle is across from the largest side. A B C 4 10 13

21. Triangle inequalities The smallest side is opposite the smallest angle and the largest side is opposite the largest angle <A = 55º, <B= 95º, <C= 30º List the sides from smallest to largest A B C

22. Triangle inequalities The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

23. Triangle inequalities Since the third side cannot be larger than the other two added together, we find the maximum value by adding the two sides. Since the third side and the smallest side given cannot be larger than the other side, we find the minimum value by subtracting the two sides.

24. Triangle relationships Congruent triangles Similar triangles Right triangles Triangle inequalities Usually 10 questions of 45 are on triangles and they start about # 15 in the test