Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Parts of a Right Triangle
Hypotenuse: longest sideLegs: Other two (2) shorter legs
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.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.2 LL Congruence Theorem
If two legs of one right triangle are congruentto the two legs of another right triangle,then the two triangles are congruent.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.3 HA Congruence Theorem
If the hypotenuse and an acute angle of one righttriangle are congruent to the hypotenuse andcorresponding acute angle of another righttriangle, then the two triangles are congruent.
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 righttriangle are congruent to the corresponding leg and acute angle of another right triangle,then the two triangles are congruent.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.5
Any point lies on the perpendicular bisectorof a segment if and only if it is equidistantfrom the two endpoints.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.6Circumcenter Theorem
The perpendicular bisectors of the sides of anytriangle are concurrent at the circumcenter,which is equidistant from each vertex of thetriangle.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.7Incenter Theorem
The angle bisectors of the angles of a triangleare concurrent at the incenter, which isequidistant from the sides of the triangle.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Definition ofAn Altitude of a Triangle
An altitude of a triangle is a segment that Extends from a vertex and is perpendicularto the opposite side.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Definition ofA Median of a Triangle
A median of a triangle is a segment extendingfrom a vertex to the midpoint of the oppositeside.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.8Orthocenter Theorem
The lines that contain the three altitudesare concurrent at the orthocenter.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.9Centroid Theorem
The three medians of a triangle are concurrentat the centroid.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Definition ofAn Exterior Angle
An exterior angle of a triangle is an angle thatforms a linear pair with one of the angles ofthe triangle.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Definition ofRemote Interior Angles
The remote interior angles of a an exterior angleare the two angles of the triangle that do notform a linear pair with a given exterior angle.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.10Exterior Angle Theorem
The measure of an exterior angle of triangleis equal to the sum of the measures of itstwo remote interior angles.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.11Exterior Angle Inequality
The measure of an exterior angle of a triangleis greater than the measure of either remoteinterior angle.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.12Longer Side Inequality
One side of a triangle is longer than another side if and only if the measure of the angle oppositethe longer side is greater than the measure ofthe angle opposite the shorter side.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.13Hinge Theorem
Two triangles have two pairs of congruent sides.if the measure of the included angle of the firsttriangle is larger than the measure of the otherincluded angle, then the opposite (third) sideof the first triangle is longer than the oppositeside of the second triangle.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.14Triangle Inequality
The sum of the lengths of any two sides of atriangle is greater than the length of the thirdside.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.15
The opposite sides of a parallelogram arecongruent.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.16SAS Congruence for Parallelograms
If two consecutive sides of a parallelogram is congruent to the corresponding consecutive sidesof another parallelogram, then the two parallelograms are congruent.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.17
A quadrilateral is a parallelogram if and onlyif the diagonals bisect one another.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.18
Diagonals of a rectangle are congruent.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.19
The sum of the measures of the four anglesof every convex quadrilateral is 360O.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.20
Opposite angles of a parallelogram arecongruent.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.21
Consecutive angles of a parallelogram aresupplementary.
Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy
Geometry
Theorem 7.22
If the opposite sides of a quadrilateral arecongruent,then the quadrilateral is a parallelogram.
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