5.2 Congruent Triangles Pythagorean Theorem Angle Bisectors Transformations Constructions Objectives: To review and practice concepts involving congruent.

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Presentation transcript:

5.2 Congruent Triangles Pythagorean Theorem Angle Bisectors Transformations Constructions Objectives: To review and practice concepts involving congruent triangles, the Pythagorean Theorem, angle bisectors, transformations, and constructions.

Proving Triangles Congruent There are six parts to all triangles. However, you only need three of them to prove congruence. However, not just any three will do. The three have to be very specific.

Included Angle The angle between two sides of a triangle is called the included angle. Included Side The side between two angles of a triangle is called the included side. Hint: think between.

Side-Side-Side (SSS) If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.

Side-Angle-Side (SAS) If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Angle-Side-Angle (ASA) If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Pythagorean Theorem a 2 + b 2 = c 2 a b c leg hypotenuse

Angle Bisectors An angle bisector cuts an angle exactly in half.

Transformations Translate – to move or slide a shape around the coordinate plane without changing it size, shape or orientation.

Transformations Reflect – to fold the shape over a straight line and create a mirror image. Does not change the size or shape but often changes the orientation. Reflect over the x-axis – swap the sign of the y-coordinate Reflect over the y-axis – swap the sign of the x-coordinate Reflect over the y = x line – swap the x and y coordinates

Transformations Rotation – moves points and shapes by turning them around a fixed point through a fixed angle. The fixed point is called the center of rotation. The fixed angle is called the angle of rotation. Rotating 180° around the origin is a simple rotation. It is the same as reflect over both the x- and y-axis. Therefore, swapping the signs of both points will rotate a point 180° around the origin.

Homework 5-2 RSG