Transcript 4.2 The case of the Missing Diagram
Slide 1
Warm Up
Slide 2
Chapter 4.2
The Case of the Missing
Diagram
Slide 3
Organize the information
in, and draw diagrams for,
problems presented in
words.
Slide 4
Set up this problem:
An isosceles triangle and the median
to the base.
Draw the shape, label everything
Write the givens and what you want
to prove.
Slide 5
Given: an isosceles triangle and
the median to the base.
Prove: The median is the
perpendicular bisector of the base.
Notice: There are two conclusions to
made:
1.The median is perpendicular to the
base.
2. The median bisects the base.
Slide 6
Now draw and label all you know.
You can label everything on the diagram
to help you make the proof.
A
Given:
ABC is isosceles
Base BC
AD is a median
B
D
Prove: BD
C
AD and bisects BC
Slide 7
NOTICE!!!
You can label everything on
a diagram to help you
make the proof.
Some problems you only have to draw,
label, write the givens and what to
prove.
Others you also have to prove.
Slide 8
Remember If….then….
Sometimes you will see these in reverse.
The medians of a triangle are congruent
if the triangle is equilateral.
Draw and set up the proof.
Write down the givens you need.
What do you need to prove?
Slide 9
X
Given: Δ XYZ is equilateral
P
Z
R
Q
Y
PY, RZ and QX are medians
~
~
Prove: PY = RZ = QX
Slide 10
The median to the base of an isosceles
triangle divides the triangle into two
congruent triangles.
Draw, write givens and what to prove,
then prove.
Slide 11
C
T
R
A
Given: Δ CAT is isosceles, with base
TA.
CR is a median.
~ Δ ARC
Prove: Δ TRC =
Slide 12
Try this one!
If each pair of opposite sides of a foursided figure are congruent, then the
segments joining opposite vertices
bisect each other.
Draw
Write Given:
Write Prove:
Write proof!
Slide 13
A
D
B
E
C
Given:
~ CD
AB =
AD ~
= BC
Prove:
AC bisects BD
BD bisects AC
Slide 14
~ Δ CDA by SSS, and thus,
Δ ABC =
= Δ DCB by SSS, and thus,
= Δ CDE by ASA, and then
AE ~
= EC and DE ~
= EB.
A
B
E
D
C
Warm Up
Slide 2
Chapter 4.2
The Case of the Missing
Diagram
Slide 3
Organize the information
in, and draw diagrams for,
problems presented in
words.
Slide 4
Set up this problem:
An isosceles triangle and the median
to the base.
Draw the shape, label everything
Write the givens and what you want
to prove.
Slide 5
Given: an isosceles triangle and
the median to the base.
Prove: The median is the
perpendicular bisector of the base.
Notice: There are two conclusions to
made:
1.The median is perpendicular to the
base.
2. The median bisects the base.
Slide 6
Now draw and label all you know.
You can label everything on the diagram
to help you make the proof.
A
Given:
ABC is isosceles
Base BC
AD is a median
B
D
Prove: BD
C
AD and bisects BC
Slide 7
NOTICE!!!
You can label everything on
a diagram to help you
make the proof.
Some problems you only have to draw,
label, write the givens and what to
prove.
Others you also have to prove.
Slide 8
Remember If….then….
Sometimes you will see these in reverse.
The medians of a triangle are congruent
if the triangle is equilateral.
Draw and set up the proof.
Write down the givens you need.
What do you need to prove?
Slide 9
X
Given: Δ XYZ is equilateral
P
Z
R
Q
Y
PY, RZ and QX are medians
~
~
Prove: PY = RZ = QX
Slide 10
The median to the base of an isosceles
triangle divides the triangle into two
congruent triangles.
Draw, write givens and what to prove,
then prove.
Slide 11
C
T
R
A
Given: Δ CAT is isosceles, with base
TA.
CR is a median.
~ Δ ARC
Prove: Δ TRC =
Slide 12
Try this one!
If each pair of opposite sides of a foursided figure are congruent, then the
segments joining opposite vertices
bisect each other.
Draw
Write Given:
Write Prove:
Write proof!
Slide 13
A
D
B
E
C
Given:
~ CD
AB =
AD ~
= BC
Prove:
AC bisects BD
BD bisects AC
Slide 14
~ Δ CDA by SSS, and thus,
Δ ABC =
= Δ DCB by SSS, and thus,
= Δ CDE by ASA, and then
AE ~
= EC and DE ~
= EB.
A
B
E
D
C