Name:
GP
Period
TRIANGLE PROPERTIES
I can define, identify and illustrate the following terms:
triangle
equilateral triangle
equiangular triangle
right triangle
interior angle
isosceles triangle
obtuse triangle
exterior angle
scalene triangle
acute triangle
vertex angle
base angle
hinge theorem
triangle inequality
hypotenuse
legs
Point of Concurrency
Equidistant
Perpendicular Bisector
Circumcenter
Angle Bisector
Incenter
Median
Centroid
Altitude
Orthocenter
Triangle Midsegment
Dates, assignments, and quizzes subject to change without advance notice.
Monday
Tuesday
Block Day
24/25
TEST 5
29
Bisectors of Triangles
Classifying Triangles
31/1
30
Medians, Centroid
Altitude, Orthocenter
Friday
26
QUIZ
Inequalities &
Exterior Angle Theorem
2
Midsegments
EQUATIONS OF
CIRCUMCENTERS AND
ORTHOCENERS
5
6
REVIEW
TEST 6
9
End of 3 weeks!
Wednesday, 10/24/12 or Thursday, 10/25/12
4-1, 4-8: Classifying Triangles
I can classify triangles by sides and angles
I can use triangle classifications to find angle measures and side lengths.
PRACTICE: : pg 219: 13-19 odd, 24-34 even 35-37 all & pg. 277: 13-19 odd, 22-26, 28-29 (24 problems)
Friday, 10/26/12
5-5, 5-6: Inequalities in One Triangle and in Two Triangles
I can apply inequalities in one triangle
I can apply inequalities in two triangles
Solve problems using the Exterior Angle Theorem
PRACTICE: pg. 228: 17-20, 45; Pg 336: 18-19, 20-30 even, 43-53 odds; and pg. 343: 9-11(all), 19-25 odds (26
problems)
Monday, 10/29/12
5-1, 5-2: Bisectors of Triangles
I can solve problems with a perpendicular bisector in a triangle.
I can identify the circumcenter.
I can solve problems using the circumcenter.
I can solve problems with an angle bisector in a triangle.
I can identify the incenter.
I can solve problems using the incenter.
PRACTICE: Pg 304: 12-18, 22-28 AND Pg 311: 12-15, 18-19, 22-34
Tuesday, 10/30/12
5-3: Median and Centroid, Altitude and Orthocenter
I can identify the median and centroid of a triangle.
I can solve problems using the centroid.
I can identify the altitude and orthocenter of a triangle.
PRACTICE: Pg 318: 12-15, 21-26, 29-37
Wednesday, 10/31/12 or Thursday, 11/1/12
5-3 and 5-3
QUIZ: Identifying Points of Concurrency
I can write the equation of perpendicular bisectors.
I can find circumcenters and orthocenters on a coordinate plane.
PRACTICE: Special Segments on the Coordinate Plane Worksheet
Friday, 11/2/12
5-4: Midsegments of Triangles
I can identify the midsegment of triangles.
I can use properties of midsegments to solve problems.
PRACTICE: Pg 325: 18-27, 30-35, 44, 45
Monday, 11/5/12
Review
PRACTICE: p 284: 4-7, 28-30 Pg 366: 5-10, 13-18, 21-24, 30-35, 37-41, 43-44
Tuesday, 11/6/12
Test: Triangle Properties
I can demonstrate knowledge of ALL previously learned material.
Score:
Classifying Triangles Examples
Ex: ▲ FIN is an equilateral
triangle. Find the value of FI.
I
You Try: Find x in the given
isosceles triangle with
AB ≅ BC
You Try: Find the value of x.
P
B
(2x + 5)
3x + 27
F
(4x – 1)
12x
N
A
C
(2x + 15)°
R
(4x - 35)°
Q
Picture Proof
1) What do you notice about the three angles of a triangle? (This is the Triangle Sum Theorem)
2) Make a conjecture about 2 and 4 .
3) What is the relationship between an exterior angle and its adjacent interior angle?
4) How is an exterior angle related to its remote interior angles? (This is the Exterior Angle Theorem)
5) How are the triangle sum theorem and the exterior angle theorem related?
Triangles on the Coordinate Plane Examples
Ex. 1 – Classify by angles and sides.
Together: D(1, 0) E(-3, -2) W(-1, 4)
You try : F(-2, 1) O(-1, 5) G(2, 5)
Ex 2 – Midsegment –
Together: A(-3, 2) B(3, 2) C(5, -2)
You try:
Ex. 3 – Medians
Together: (-3, 2) (1, -6) (5, -2)
You try:
Where is the centroid?
Ex 4 – Altitude
Together:
(-2, 5) (6, 5) (4, -1)
You try:
Where is the orthocenter?
Ex. 5 – Perpendicular Bisectors
Together: (3, 3) (3, -1) (-3, -3)
Where is the circumcenter?
You try :
Name ______________________________________ Period _______________
Special Segments on a Coordinate Plane
Classify the following triangles. Be sure to justify each classification.
1. A(1, 3) B(3, -1) C(5, 3)
2. D(-2, 3) E(4, 5) F(0, -3)
Using the points given, draw in each median. State the location of the centroid of each triangle.
3. G(-1, -3) H(7, 1) J(3, 5)
4. K(-3, 5) L(3, 1) M(-5, -3)
Using the points given, draw in each altitude. State the location of the orthocenter of each triangle.
5. (-2, 0) (4, 0) (2, 4)
6. (-3, 1) (3, 1) (1, 5)
Using the points given, draw in each perpendicular bisector. State the location of the circumcenter for
each triangle.
7. (-2, -1) (2, -3) (0, 3)
8. (-3, -2) (1, 6) (5, -2)
Using the points given, draw each midsegment. Then show that the midsegments are parallel and ½
the length of the sides.
9. A(1, 3) B(3, -1) C(5, 3)
10. D(-2, 3) E(4, 5) F(0, -3)
SPECIAL
SEGMENT
Perpendicular
Bisector
Altitude
Angle
Bisector
Median
Midsegment
DEFINITION
DRAWING
POINT OF
CONCURRENC
Y
OTHER
INFORMATI
ON