1. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry

2. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Parts of a Right Triangle Hypotenuse: longest side Legs: Other two (2) shorter legs

3. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.1 HL Congruence Theorem If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the two triangles are congruent.

4. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.2 LL Congruence Theorem If two legs of one right triangle are congruent to the two legs of another right triangle, then the two triangles are congruent.

5. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.3 HA Congruence Theorem If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the two triangles are congruent.

6. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.4 LA Congruence Theorem If a leg and one of the acute angles of a right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the two triangles are congruent.

7. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry

8. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.5 Any point lies on the perpendicular bisector of a segment if and only if it is equidistant from the two endpoints.

9. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.6 Circumcenter Theorem The perpendicular bisectors of the sides of any triangle are concurrent at the circumcenter, which is equidistant from each vertex of the triangle.

10. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.7 Incenter Theorem The angle bisectors of the angles of a triangle are concurrent at the incenter, which is equidistant from the sides of the triangle.

11. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Definition of An Altitude of a Triangle An altitude of a triangle is a segment that Extends from a vertex and is perpendicular to the opposite side.

12. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Definition of A Median of a Triangle A median of a triangle is a segment extending from a vertex to the midpoint of the opposite side.

13. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.8 Orthocenter Theorem The lines that contain the three altitudes are concurrent at the orthocenter.

14. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.9 Centroid Theorem The three medians of a triangle are concurrent at the centroid.

15. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry

16. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Definition of An Exterior Angle An exterior angle of a triangle is an angle that forms a linear pair with one of the angles of the triangle.

17. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Definition of Remote Interior Angles The remote interior angles of a an exterior angle are the two angles of the triangle that do not form a linear pair with a given exterior angle.

18. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.10 Exterior Angle Theorem The measure of an exterior angle of triangle is equal to the sum of the measures of its two remote interior angles.

19. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.11 Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.

20. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry

21. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.12 Longer Side Inequality One side of a triangle is longer than another side if and only if the measure of the angle opposite the longer side is greater than the measure of the angle opposite the shorter side.

22. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.13 Hinge Theorem Two triangles have two pairs of congruent sides. if the measure of the included angle of the first triangle is larger than the measure of the other included angle, then the opposite (third) side of the first triangle is longer than the opposite side of the second triangle.

23. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry

24. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.14 Triangle Inequality The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

25. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.15 The opposite sides of a parallelogram are congruent.

26. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.16 SAS Congruence for Parallelograms If two consecutive sides of a parallelogram is congruent to the corresponding consecutive sides of another parallelogram, then the two parallelograms are congruent.

27. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.17 A quadrilateral is a parallelogram if and only if the diagonals bisect one another.

28. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.18 Diagonals of a rectangle are congruent.

29. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.19 The sum of the measures of the four angles of every convex quadrilateral is 360 O.

30. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.20 Opposite angles of a parallelogram are congruent.

31. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.21 Consecutive angles of a parallelogram are supplementary.

32. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.22 If the opposite sides of a quadrilateral are congruent,then the quadrilateral is a parallelogram.

33. Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy Geometry Theorem 7.23 A quadrilateral with one pair of parallel sides that are congruent is a parallelogram.