Transcript CPCTC

Use Congruent Triangles
1.
2.
Objectives:
To use congruence
shortcuts and CPCTC
to show that
segments and angles
are congruent
To construct
flowcharts to illustrate
the logical flow of an
argument
Assignment:
• P. 166: 12-19
• P. 177-178: 1-11
• Challenge Problems
Objective 1
You will be able to use
congruence shortcuts and
CPCTC to show that
segments and angles are
congruent
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
to explain away that little bit
of geometric sorcery.
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.
Example 1
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
Parts of
Congruent
Triangles are
Congruent
Objective 2
You will be able to construct flowcharts to
illustrate the logical flow of an argument
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
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
Within your group, 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.
The Proof Game! Round 2
Here’s your chance to play the game that is
quickly becoming a favorite among America’s
teenagers: The Proof Game!
In this round, your group will be given one
problem to prove. You are to collaborate with
your group members to complete the proof.
Then you must choose someone to present
said proof to the class. The most significant
contributor will earn a delicious reward!
Proof Game: Round 2
1.
Proof Game: Round 2
2.
Proof Game: Round 2
3.
Proof Game: Round 2
4.
Use Congruent Triangles
1.
2.
Objectives:
To use congruence
shortcuts and CPCTC
to show that
segments and angles
are congruent
To construct
flowcharts to illustrate
the logical flow of an
argument
Assignment:
• P. 166: 12-19
• P. 177-178: 1-11
• Challenge Problems