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Unit 4: Triangles and Coordinate Proof (4.7) p.243­250
Ex: Draw a right triangle on the coordinate plane below that has side lengths of 6 and 8. Now find the hypotenuse. 1
Ex: If triangle ABC ≅ triangle DBC, find the coordinates of point B using the picture below and explain how you know. A (0,7)
B
C (0,0)
D (7,0)
2
Ex: Explain how you know the x­axis bisects <ABC
A (0,4)
D (0,0)
B (6,0)
C (0,­4)
3
HW: p.246­248
#4,5,12,13,14,15
#18­21
4
Unit 4: Inequalities in One Triangle (5.5) p.295­301
Theorem:
One side of a triangle is longer than another side IFF the angle opposite the longer side is larger than the angle opposite the shorter side.
B
106o
BC<AC
A
27o
C
D
E
6
8
F
m<D > m<E
5
Exterior Angle Inequality: The measure of an exterior angle is greater than the measure of either of the two nonadjacent interior angles.
A
m<1 > m<A m<1 > m<B
1
B
6
Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. A
AB + BC > AC
AB + AC > BC
BC + AC > AB
B
C
7
Ex: Write the measures of the sides/angles from least to greatest.
T
Y
a)
5
b)
7
X
22o
U
Z
10 31o
V
8
Ex: Determine if the triangle can have the given lengths and explain why/why not? a) 3, 7, 10
b) 4, 14, 17
9
Ex: Determine all possible lengths for the 3rd side of a triangle given two lengths.
a) 4, 17, ?
b) 15, 21, ?
10
Ex: Determine if the triangle is a right triangle and classify it by it side lengths.
B (0,7)
C (­3,1)
A (10,2)
11
HW: p.298­299
#6­18 even
#24­28 all
12