Transcript congruent triangles

Warm-Up
Recall that an angle bisector
is a ray that divides the
angle into two congruent
parts. We will use the
magic of a compass and
straightedge to create one
of these divisive rays and
then use congruent triangles
Bisect an Angle
1. Draw an acute angle and label the vertex
A.
Bisect an Angle
2. Using vertex A as the center, draw an arc
intersecting both sides of your angle. Label the
intersections B and C.
Bisect an Angle
3. Using the same compass setting, draw two
intersecting arcs in the interior of your angle,
one centered at B, the other centered at C.
Bisect an Angle
4. Label the intersection D.
Bisect an Angle
5. Draw a ray from vertex A through point D.
Bisect an Angle Video
Click on the button below to watch
a video on how to bisect an angle
4.6 Use Congruent Triangles
Objectives:
1. To use congruence shortcuts and
CPCTC to show that segments and
angles are congruent
2. To construct flowcharts to illustrate the
logical flow of an argument
Example 1
Review: Congruence Shortcuts
Congruent Triangles (CPCTC)
Two triangles are congruent triangles if and
only if the corresponding parts of those
congruent triangles are congruent.
• Corresponding
sides are
congruent
• Corresponding
angles are
congruent
Flow Chart
A flow chart is a
concept map that
shows a step-bystep procedure
through a
complicated system.
Boxes represent
actions, and arrows
connect to the boxes
to show the flow of
action.
Example 2
1. AC  AB
Given
Given :
AC  AB
CD  BD
Prove : CAD  BAD
2. CD  BD
Given
3. AD  AD
Reflexive
Property
4. ACD  ABD
SSS 
Postulate
5. CAD  BAD
CPCTC
Investigation 1
In your notebook, make a flow-chart proof to
show that segment AD is congruent to
segment BC.
Investigation 1
Remember, first show that the triangles are
congruent with a shortcut, then use
CPCTC to show the segments are
congruent.