Download 6.6-6.7 Isosceles Triangles, Altitudes and

6.6/6.7 Isosceles Triangles, Altitudes and
Medians
Learning Objective: To apply the Isosceles triangle theorem and its
converse, write proofs using isosceles triangles, and to identify and explore
the properties of medians and altitudes.
Warm-up (IN)
Complete with < or >.
B
65º
1. AB___BC
<
2. BC___AC
<
A 60º
55º
Solve each equation.
3. 4x  6  3x  9 15
4. 5x 11  x  3 2
5. 9x  12x  4 4/3
C
Learning Objective: To apply the Isosceles triangle theorem and its converse, write
proofs using isosceles triangles, and to identify and explore the properties of medians
and altitudes.
Notes
Isosceles Triangle Theorem -
If 2 sides of a triangle are congruent, then the angles
opposite those sides are congruent.
A
If AT  AD, then T  D.
Vertex
angle
legs
Converse -
T
Base
angles
base
D
If 2 angles of a triangle are
congruent, then the sides opposite
those angles are congruent.
Learning Objective: To apply the Isosceles triangle theorem and its converse, write
proofs using isosceles triangles, and to identify and explore the properties of medians
and altitudes.
EX 1 – Given: AB  CB
AE  CD
Prove: 1  2
B
Paragraph proof!!
A
1
D
2
E
C
If AB  CB, then A  B, by the Isosceles  Thm.
Because it's given that AB  CB and AE  CD,
ABE  CBD by the SAS postulate.
Therefore, BE  BD because of CPCTC. So 1  2, by
the Isosceles  Thm.
Learning Objective: To apply the Isosceles triangle theorem and its converse, write
proofs using isosceles triangles, and to identify and explore the properties of medians
and altitudes.
Median of a Triangle Segment from a vertex to the midpoint of the opposite
side
Altitude of a Triangle A perpendicular segment from a vertex to the line that
contains the opposite side.
Learning Objective: To apply the Isosceles triangle theorem and its converse, write
proofs using isosceles triangles, and to identify and explore the properties of medians
and altitudes.
*In an isosceles triangle, the median, altitude and angle
bisector (from the vertex angle) are all the same
segment.
Learning Objective: To apply the Isosceles triangle theorem and its converse, write
proofs using isosceles triangles, and to identify and explore the properties of medians
and altitudes.
EX 2 –
In ABC , mAEC  65 , AC  AE ,
C
B
5
X
A
AD is and altitude, and BE bisects AEC.
D Find each measure or length. Explain your
reasoning.
E
a. mDXE
b. CE
CKC p. 321!! On separate
paper!
Out – Compare and contrast the altitude and the
median of a triangle.
POW!!
Summary – Today, I understand…
Or I’m not too sure about…
HW – p. 317#9-15 odd, 20,
p. 322 #1,2,6,7,11,12