Name _________________________________________ Period ____ 10/22 – 11/1
G
G
E
E
O
O
M
M
E
E
T
T
R
R
Y
Y
U
U
N
N
I
I
T
T
5
5
–
–
T
T
R
R
I
I
A
A
N
N
G
G
L
L
E
E
P
P
R
R
O
O
P
P
E
E
R
R
T
T
I
I
E
E
S
S
Vocabulary Terms: Acute Triangle Right Triangle Obtuse Triangle Scalene Isosceles Equilateral Equiangular Interior Angle Exterior Angle Auxiliary Line Vertex Side Remote Interior Angle Leg Base Base Angle Opposite Vertex Angle Height Altitude Midsegment Perpendicular Bisector Angle Bisector Median Centroid Incenter Orthocenter Circumcenter Inequalities Range of numbers Inscribed Circumscribed Point of Concurrency 10/22Classify and Triangle Angle Theorems
10/23
Isosceles and Equilateral
10/24 – 25
Special Segments
10/26
Special Segment Proofs
10/29 Triangle Inequalities 10/30 Review 10/31 – 11/1
Test
Monday, 10/22Chapter 4 Section 1 and 2: Classifying Triangles and Interior and Exterior Angle Theorem I can classify a triangle by its sides or angles.
I can solve problems involving the interior triangle sum theorem. I can solve problems involving the exterior triangle theorem
ASSIGNMENT: Pg. 219 #1-2, 12-17, 23-28, 34-37 & pg. 227 #2, 4-11, 23-24, 29-35 Completed: Tuesday, 10/23
Chapter 4 Section 8: Isosceles and Equilateral Triangle Properties I can solve problems using the isosceles triangle properties
I can solve problems using the equilateral triangle properties.
ASSIGNMENT: Pg. 276 (#1-7, 10, 12-13, 22-26, 28, 33-34, 44) Completed: Wednesday or Thursday, 10/24 – 25
Chapter 5 Section 1 – 4 : All Special Segments I can solve problems using the midsegment of a triangle
I can find the point(s) of concurrency of a triangle
I can solve problems using the centroid, circumcenter, or incenter of a triangle.
ASSIGNMENT: Special Segments in Triangles Worksheet Completed:
Friday, 10/26
Chapter 5 Section 1 – 4 : All Special Segments I can use the coordinate plane to represent geometric figures.
I can use logical reasoning to prove statements are true or find a counter example to prove them false. I can provide and recognize a valid deductive argument.
Monday, 10/29
Chapter 5 Section 5 : Inequalities in 1 Triangle I can determine if 3 segments will make a triangle
I can provide a range of answers given 2 sides of a triangle.
I can order the sides of a triangle given the angles and order the angles given the sides.
ASSIGNMENT: Pg. 336 (4-15, 32-33, 35-38, 42-53, 71) Completed:
Tuesday, 10/30
Wednesday or Thursday, 10/31 – 11/1
If you miss the review day, you are still expected to take the test on the test day.
For more help BEFORE the test:
1. Use the indicated chapters in your book
2. Use the book online (it has videos and a homework help section)
3. Use Google to find more resources
4. Come to tutoring (with assignment)
Review Day
ASSIGNMENT:
Review Worksheet Completed:Test Day
Day 1
Classifying Triangles 1. Classify the triangles below based on their angle measures.2. Classify the triangles below based on their side lengths. Diagram the triangles.
Important Note: In an __________________ triangle, all 3 angles are _________________.
Triangle Sum Theorem and Exterior Angle Theorem The sum of all _______________ angles in a triangle is ______________.
Ex: One acute angle of a right triangle measures 22.9⁰. Find the measure of the other acute angle.
You Try: Find the measure of the missing angle. You Try: Find the measure of the missing angles.
The measure of an __________________ angle of a triangle is equal to the sum of its ______________________ __________________ angles.
Ex: Find the measure of Ex: Find the measure of You Try: Solve for x. 37⁰
47⁰
Day 2
Isosceles and Equilateral Triangles
Objectives:Prove theorems about isosceles and equilateral triangles. Apply properties of isosceles and equilateral triangles. Vocabulary:
legs of an isosceles triangle vertex angle
base base angles
ISOSCELES TRIANGLES
Example 1: Astronomy Application The length of YX is 20 feet.
Explain why the length of YZ is the same.
Example 2A: Finding the Measure of an Angle Find m∠∠∠F. ∠
Example 2B: Finding the Measure of an Angle Find m∠∠∠G. ∠
EQUILATERAL TRIANLGES
Example 3A: Using Properties of Equilateral Triangles Find the value of x.
Example 3B: Using Properties of Equilateral Triangles Find the value of y.
2.5
Day 3
Special Segments PracticeI. Matching: Match the picture to the special segment. You will use the special segment more than once. 1) Midsegment
2) Altitude 3) Angle Bisector
4) Perpendicular Bisector 5) Median
II. Matching: Match the point of concurrency to the special segment and to the correct fact about location. 6) Orthocenter A) Medians i) Equidistant from verticies 7) Incenter B) Altitudes ii) Equidistant from sides
8) Circumcenter C) Angle Bisectors iii) 2(small section) = (larger section) 9) Centroid D) Perpendicular Bisectors iv) No location fact
III. Solve: Use the properties of special segments to solve the following problems. 10) Find WY, ZY, and XY 11) N is the circumcenter.
Find QN, RN, QR
12) Use the picture at the right to answer the following questions. a) A segment parallel to
b) A segment that has half the length of c) A segment that has twice the length of
13) In the diagram of ΔABC shown below, D is the midpoint of , E is the midpoint of , and F is the midpoint of .
If AB = 20, BC = 12, and AC = 16, what is the perimeter of trapezoid ABEF? A 24 B 36 C 40 D 44 A B C D E G F H I J AB
BC
AC
AC
AC
EC
14) G is the centroid. If CG = 20, find GE and CE?
15) In ΔABC shown below, P is the centroid and BF = 18. What is the length of BP? A 6 B 9 C 3 D 12
Use the picture to the right for 16 and 17. 16) If DF = 13, what is DE?
17) Find m<DAG and m<GAE
18) Find m<XRQ, m<PRQ, and m<PQR.
19) Find n 20) Y is the circumcenter. Find YC and AB.
21)
22) The circumcenter of the triangle is equidistant from the ________________ of the triangle. 23) The incenter is important because it is _______________________ from the sides of the triangle. 24) Use the picture at the right to answer the following questions.
a) ST ______ d) QR ______ b) PU ______ e) m<SUP ______ c) M<SUR _______ f) m<PRQ
15 mEAD = °
25.
26.
Day 4
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 –
Ex. 3 – Medians
Together: (-3, 2) (1, -6) (5, -2) You try: Find the other 2 medians.
Where is the centroid? Ex 4 – Altitude
Together: (-2, 5) (6, 5) (4, -1) You try: Find the other 2 altitudes.
Where is the orthocenter? Ex. 5 – Perpendicular Bisectors
Together: (3, 3) (3, -1) (-3, -3) You try : Find the other 2 perpendicular bisectors.
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.
NAME____________________________________DATE_________________PER.________ TRIANGLE INEQUALITY PROPERTIES NOTES
Is it possible for a triangle to have sides with the following lengths? If YES, classify the triangle by its sides. 1. YES or NO Classification:____________________ Side lengths: 20, 9, 8 2. YES or NO Classification:____________________ Side lengths: 3, 4, 5 3. YES or NO Classification:____________________ Side lengths: 9, 12, 15 4. YES or NO Classification:____________________ Side lengths: 6, 6, 20
Given two sides of a triangle, state the range of possible values for the third side of the triangle.
6. __________________ Side lengths: 13 and 24
7. __________________ Side lengths: 6 and 21
List the segments in the following triangles shortest to longest.
8. __________ 10. __________ A B C 70° 65° A B C 40° 40°
11. __________
List the angles in the following triangles from largest to smallest.
12. __________ 13. __________ A B C 150° 10° C B A 11 12 13 X Z Y 1 4 2
