Download 5.2 Notes - West Ada

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
2
2
2
a +b =c
c
a leg
leg
b
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