TRIANGLE CONGRUENCE

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TRIANGLE CONGRUENCE by Mind Map: TRIANGLE CONGRUENCE

1. 4-1 CONGRUENCE AND TRANSFORMATIONS

1.1. HOW ARE TRANSFORMATIONS MADE AND DESCRIBED IN THE COORDINATE PLANE?

1.2. A DILATION WITH SCALE FACTOR K > 0 AND CENTER (0,0) MAPS (x,y) TO (kx,ky)

1.3. ISOMETRY IS A TRANSFORMATION THAT PRESERVES LENGTH, ANGLE, MEASURE, AND AREA.

1.3.1. A RIGID TRANSFORMATION IS ANOTHER NAME FOR ISOMETRY

2. 4 - 1 CLASSIFYING TRIANGLES

2.1. TYPES OF TRIANGLES

2.1.1. - ACUTE TRIANGLE - EQUILANGULAR TRIANGLE - RIGHT TRIANGLE - OBTUSE TRIANGLE - EQUILATERAL TRIANGLE - ISOSCELES TRIANGLE - SCALENE TRIANGLE

3. 4-3 ANGLE RELATIONSHIPS IN TRIANGLES

3.1. THE SUM OF THE ANGLE MEASURES OF A TRIANGLE IS 180 DEGREES

3.1.1. AN AUXILIARY LINE IS A LINE THAT IS ADDED TO A FIGURE TO AID IN A PROOF.

3.2. A COROLLARY IS A THEOREM WHOSE PROOF FOLLOWS DIRECTLY FROM ANOTHER THEOREM.

3.2.1. THE INTERIOR IS THE SET OF ALL POINT S INSIDE THE FIGURE. THE EXTERIOR IS THE SET OF ALL POINTS OUTSIDE THE FIGURE.

4. 4-4 CONGRUENT TRIANGLES

4.1. CORRESPONDING ANGLES ARE THE SAME POSITION IN POLYGONS WITH AN EQUAL NUMBER OF SIDES

4.2. A POLYGON IS CONGRUENT IF THEIR CORRESPONDING SIDES ARE CONGRUENT OF 2 POLYGONS

4.3. A HELPFUL HINT IS THAT 2 VERTICES THAT ARE THE ENDPOINTS OF A SIDE ARE CALLED CONSECUTIVE VERTICES

4.3.1. YOU CAN NAME CONGRUENT CORRESPONDING PARTS BY IDENTIFYING ALL PAIRS OF CORRESPONDING CONGRUENT PARTS.

5. 4-5 TRIANGLE CONGRUENCE SSS AND SAS

5.1. TRIANGLE RIGIDITY GIVES YOU A SHORTCUT FOR PROVING Z TRIANGLES CONGRUENT

5.1.1. YOU NEED TO REMEMBER ADJACENT TRIANGLES SHARE A SIDE, SO YOU CAN APPLY THE REFLECTIVE PROPERTY TO GET A PAIR OF CONGRUENT PARTS