joseph angelo tiongson. copyright 2009. discovery christian academy geometry

Joseph Angelo Tiongson. Copyright 2009. Discovery Christian Academy

Geometry


Geometry

Parts of a Right Triangle

Hypotenuse: longest sideLegs: Other two (2) shorter legs


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.


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.


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.


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.


Geometry


Geometry

Theorem 7.5

Any point lies on the perpendicular bisectorof a segment if and only if it is equidistantfrom the two endpoints.


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.


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.


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.


Geometry

Definition ofA Median of a Triangle

A median of a triangle is a segment extendingfrom a vertex to the midpoint of the oppositeside.


Geometry

Theorem 7.8Orthocenter Theorem

The lines that contain the three altitudesare concurrent at the orthocenter.


Geometry

Theorem 7.9Centroid Theorem

The three medians of a triangle are concurrentat the centroid.


Geometry


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.


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.


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.


Geometry

Theorem 7.11Exterior Angle Inequality

The measure of an exterior angle of a triangleis greater than the measure of either remoteinterior angle.


Geometry


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.


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.


Geometry


Geometry

Theorem 7.14Triangle Inequality

The sum of the lengths of any two sides of atriangle is greater than the length of the thirdside.


Geometry

Theorem 7.15

The opposite sides of a parallelogram arecongruent.


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.


Geometry

Theorem 7.17

A quadrilateral is a parallelogram if and onlyif the diagonals bisect one another.


Geometry

Theorem 7.18

Diagonals of a rectangle are congruent.


Geometry

Theorem 7.19

The sum of the measures of the four anglesof every convex quadrilateral is 360O.


Geometry

Theorem 7.20

Opposite angles of a parallelogram arecongruent.


Geometry

Theorem 7.21

Consecutive angles of a parallelogram aresupplementary.


Geometry

Theorem 7.22

If the opposite sides of a quadrilateral arecongruent,then the quadrilateral is a parallelogram.


Geometry

Theorem 7.23

A quadrilateral with one pair of parallel sidesthat are congruent is a parallelogram.

joseph angelo tiongson. copyright 2009. discovery christian academy geometry

Documents

angles ofthe triangle

angle thatforms

acute angles

right trianglehypotenuse

ll congruence theoremif

ha congruence theoremif

la congruence theoremif

centroid theoremthe