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.

Write all 3 triangle congruence properties you learned last year. ■SSS –If 3 sides of 2 different triangles are congruent, the two triangles are congruent. ■SAS –If two sides and the angle between the sides are congruent in different triangles, the two triangles are congruent. ■ASA –If two angles and the side between the two angles are congruent in different triangles, those triangles are congruent.

Say whether the triangles are congruent, if so, state why. No AAA Side lengths might not be congruent.

Pythagorean Theorem a 2 + b 2 = c 2 a b c leg hypotenuse Used to find the missing side of a triangle. Can only be used for right triangles.

Find the length of the missing sides.

Perpendicular Bisector ■A line that intersects another segment at a right angle and splits that segment into two equal pieces ■Draw a line segment with endpoints ■Put compass needle on one point and draw a half circle. –Compass needs to be over half as long as the segment. ■Repeat the process from the other endpoint. –Make sure you don’t change the distance on your compass. ■Find the points where the arcs intersect. ■Draw a line through those two points. ■This line is the perpendicular bisector. –Label your right angles. –Label each half congruent

Angle Bisectors ■A ray which cuts an angle into two congruent angles ■Make an angle. ■Put the compass needle on the vertex ■ Make an arc with your compass so that it intersects both sides of the angle. –Length does not matter. ■Move compass needle to one of the intersection points ■Draw an arc somewhere in the middle of the angle ■Repeat process from the other intersection point. –Be sure to keep lengths the same for this part. –These two arcs should intersect in the middle of the angle. ■Draw a ray from the vertex of the angle through the intersection point ■Label the congruent angles.

Transformations ■ Translation – to move or slide a shape left, right, up, or down. ■ Reflection – Folding the image over a given line. ■ Rotation – Moving an image around a given point.

Reflections ■ Over the x-axis – y-coordinate changes sign ■ Over the y-axis – x-coordinate changes sign ■ Over the y = x line – find the inverse of the points Rotations ■ Rotation of 180° (around the origin) - Same as reflecting over x-axis and y-axis. Switch signs on both coordinates.

Translation, reflection or rotation?