Download Week 1 and 2 Review

Aim: Week 1 and 2 Concept Review (QUIZ AT 10:30!)
Do Now: Copy the image and Complete the following "statement reason" proofs .
Given: AD|| EH.
a. Prove that <ABE ≅ <BEF
b. Prove that <EBF ≅ <GCH
c. Prove that triangle CGH is a right triangle. (Requires at least 2
steps)
Using the Segment Addition
Postulate
If EG = 100, find the value of x. Then find EF and FG.
4x - 20
E
2x + 30
F
G
Find the missing complementary
angle.
?°
64°
The following angles are complementary.
Solve for x.
2x + 5
The following angles are supplementary.
Solve for x.
2x + 10
3x + 20
In the figure a || b.
1. Name the angles congruent to 3.
2. Name all the angles supplementary to 6.
3. If m1 = 105° what is m3?
4. If m5 = 120° what is m2?
5. Name a pair of
a. Alternate exterior angles
b. Alternate interior
c. Corresponding
d. Vertical
Find the missing angles.
45
°
Hint: The 3 angles
in a triangle sum to
180°.
d°
b°
50
°
75
°
Another practice problem
40
°
120°
Find all the missing
angle measures,
and name the
postulate or
theorem that
gives us
permission to
make our
statements.
Related Regents Question
• A transversal intersects two lines. Which
condition would always make the two lines
parallel?
• 1)Vertical angles are congruent.
• 2)Alternate interior angles are congruent.
• 3)Corresponding angles are supplementary.
• 4)Same-side interior angles are
complementary.
Related Regents Question
In the diagram above, line p intersects line m and line n.
If <1 = 7x and <2 = 5x+30 , lines m and n are parallel
when x equals
1) 12.5
2) 15 3) 87.5
4) 105
Ex. : Interior Angles of a
Quadrilateral
P
• Find the measure of
each angle in the
quadrilateral?
80°
70°
x°
Q
2x°
R
S
Example: Find m<1
Find m<2
Find m<3
82
28
1
2
68
3
Example
The diagram is a map showing John's house, Kay's
house, and the grocery store. What is the angle the
two houses make with the store?
y = 12, Store = 30°
Think-Pair-Share
• Can a right triangle contain an obtuse angle?
• Explain.
Related Regents Questions
• The degree measures of the angles of Triangle
ABC are represented by x, 3x, and . Find the
value of x.
Related Regents Questions
DEF is a right triangle , <D = 90 and <F is 12
degrees less than twice <E. Find E and F .
Example: Applying the Third Angles Theorem
Find mP and mT.
Ex. 3 Finding an Angle
Measure.
Exterior Angle theorem: m1 = m A +m
1
65

x
(2x+10)
18
Example
Find mACD.
Regents Question
Related Regents Questions
• What is the measure of <LKN?
Mid-Segments
•
•
•
•
•
Given: Segment FE is the mid-segment of triangle ABC.
Point D is the midpoint of BC.
m∠ FAE = 75° and m∠ FEC = 120°
AF = 5.6 ft., EC = 4.5 ft., and BC = 12.5 ft
Fill in all missing information.
Related Regents Questions
• In the diagram above, D is the midpoint of AC, O is the
midpoint of AT, and G is the midpoint of CT.
• If AC = 10, AT = 18, and CT = 22, what is the perimeter
of parallelogram CDOG?
Related Regents Questions
• Find the perimeter of the triangle formed by
connecting the midpoints of the sides of
Triangle ABC
Khan Academy Week 1 & 2
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Recognizing rays lines and line segments
Parallel lines 1
Points lines and planes
Combining like terms
Combining like terms with distribution
Alternate exterior angles
Same side exterior angles
Alternate exterior angles 2
Same side exterior angles 2
Segment Addition
Midpoint of a Segment