Download - Problem of the Day (Monday)
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Problem of the Day (Monday)
Alternate Interior Angles?
a. 3 & 6, 4 & 5
b. 1 & 4, 2 & 3, 5 & 8, 7 & 6
c. 1 & 5, 2 & 6, 3 & 7, 4 & 8
d. 1 & 8, 2 & 7
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Angles ReviewCorresponding Angles?
a. 1 & 2, 2 & 4, 3 & 4, 1 & 36 & 5, 6 & 8, 7 & 8, 5 & 7
b. 1 & 4, 2 & 3, 5 & 8, 7 & 6
c. 1 & 5, 2 & 6, 3 & 7, 4 & 8
d. 1 & 8, 2 & 7
1 23 4
7
6
8
5
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Supplementary Angles?
a. 1 & 2, 2 & 4, 3 & 4, 1 & 36 & 5, 6 & 8, 7 & 8, 5 & 7
b. 1 & 4, 2 & 3, 5 & 8, 7 & 6
c. 1 & 5, 2 & 6, 3 & 7, 4 & 8
d. 1 & 8, 2 & 7
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Alternate Exterior Angles?
a. 1 & 2, 2 & 4, 3 & 4, 1 & 36 & 5, 6 & 8, 7 & 8, 5 & 7
b. 1 & 4, 2 & 3, 5 & 8, 7 & 6
c. 1 & 5, 2 & 6, 3 & 7, 4 & 8
d. 1 & 8, 2 & 7
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Vertical Angles?
a. 1 & 2, 2 & 4, 3 & 4, 1 & 36 & 5, 6 & 8, 7 & 8, 5 & 7
b. 1 & 4, 2 & 3, 5 & 8, 7 & 6
c. 1 & 5, 2 & 6, 3 & 7, 4 & 8
d. 1 & 8, 2 & 7
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Polygon:
Closed figure
Regular Polygon:
All sides are equal
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Triangles Everywhere
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Problem of the Day (Tuesday)
What is the measure of angle x?
a. 720°
b. 120°
c. 360°
d. 60°
x
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A regular pentagon:
1. What is the sum of the interior angles?
2. What is the measure of each interior angle?
3. What is the sum of the exterior angles?
4. What is the measure of each exterior angle?
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An irregular pentagon
What is the measure of the missing angle?
90˚
90˚
130˚
130˚
?
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A regular hexagon:
1. What is the sum of the interior angles?
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What is the measure of the missing angle?
170˚
90˚ 120˚
100˚
130˚?
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A regular octagon:
1. What is the sum of the interior angles?
2. What is the measure of each interior angle?
3. What is the sum of the exterior angles?
4. What is the measure of each exterior angle?
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A regular decagon:
1. What is the sum of the interior angles?
2. What is the measure of each interior angle?
3. What is the sum of the exterior angles?
4. What is the measure of each exterior angle?
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Missing Angles Challenge
110°
45°
Name__________________
a
bc
d
e
f
*You may only assume that the pentagon and hexagon are regular.
gh
i
jk
lm
n
o p
q
r
s t
u vx
a = _____b = _____c = _____d = _____e = _____f = _____g = _____h = _____i = _____j = _____k = _____l = _____m = _____n = _____o = _____p = _____q = _____r = _____s = _____t = _____u = _____v = _____w = _____x = _____
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Learning Target
I can…
Find the exterior angles of any polygon
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Exterior Angles of a Polygon
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Level Five – Find the missing angles1.
ab
2.
3.
4. 34˚
ba
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Missing Angles
The lines m and n are parallel
What is the measure angle b?
What is the measure of angle a?
What is the measure of angle g?
What is the measure of angle f?
98°ab c
de
fg
m n
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Create your own puzzleRules:1. You must use at least 2 regular
polygons2. Angle measures must be close (they do
not have to be perfectly drawn to scale)3. You must use a ruler4. You must include 3 of the following:
complementary angles, supplementary angles, interior angles, exterior angles, corresponding angles, vertical angles
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Problem of the Day (Tuesday)
What is the measure of angle x?
a. 720°
b. 120°
c. 360°
d. 60°
x
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A regular pentagon:
1. What is the sum of the interior angles?
2. What is the measure of each interior angle?
3. What is the sum of the exterior angles?
4. What is the measure of each exterior angle?
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Congruent Triangles• All sides are congruent and all angles are
congruent
G
H
I
J
K
L
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Congruent Triangles
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SSS
A
B
C D
E
F
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SAS
G
H
I
J
K
L
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ASA
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AAS
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SQ VT Side Q E Angle
QP EY Side
Q Y Angle
Congruent PolygonsCongruent Polygons
Show that each pair of triangles is congruent.
QPR EYT by ASA. SQR VTU by SAS.
b.a.
Q T Angle
QR TU Side
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Does AAA guarantee that two triangles are congruent? Why or
why not?
No
Same angles, different sizes
Example:
50° 50°
80°
50° 50°
80°
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Congruent PolygonsCongruent Polygons
A surveyor drew the diagram below to find the distance from
J to I across the canyon. Show that GHI KJI. Then find JK.
J H Both are right angles.
JI HI Both measure 48 ft.
KIJ GIH They are vertical angles.
So ∆GHI ∆ JI by ASA
Corresponding parts of congruent triangles are congruent.JK corresponds to HG, so JK is 36 ft.
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Congruent PolygonsCongruent Polygons
Use ABC and XYZ to answer the questions.
1.Suppose AC= XZ, AB = XY, and BC = YZ. Write a congruence statement for the figures.
2.Suppose ABC and XYZ are congruent. If AB = 5 cm, BC = 8 cm, and AC = 10 cm, find XZ.
3. Suppose B Y, A X, and AB XY. Why is ABC XYZ?
∆ABC ∆XYZ
10 cm
ASA
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Congruent PolygonsCongruent Polygons
4. Let AB = XY = 9 inches; BC = YZ = 24 inches; and m B = 85°, m Z = 35°, and m Y = 85°. Prove that the triangles are congruent and find m C.
∆ABC ∆XYZ by SAS; m C =35°
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Problem of the Day (Wednesday)
Are the two triangles congruent? Why?
a. Yes, because of SAS
b. Yes, because of ASA
c. Yes, because of SSS
d. No, because two side are congruent, no angles
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aa ABC is congruent to DCB because of SAS
aa ABC is congruent to DCB because of SAS
aa ABC is congruent to BCD because of AAS
d. The triangles are not congruent because they only have a side and angle that are congruent
A
B
C
D
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Are the two triangles congruent? Why or why not?
a. Yes, because of SAS
b. Yes, because of ASA
c. Yes, because of SSA
d. No, because SSA is not a congruent triangle rule
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Review
Are the two triangles congruent? Why?
a. Yes, because of SAS
b. Yes, because of ASA
c. Yes, because of SSS
d. No, because two side are congruent, no angles
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Are the two triangles congruent? Why?
a. Yes, because of SAS
b. Yes, because of ASA
c. Yes, because of SSS
d. No, because two side are congruent, no angles
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Are the two triangles congruent? Why?
a. Yes, because of AAS
b. Yes, because of ASA
c. Yes, because of SSS
d. No, because two sides are congruent, no angles
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Is ? Why?
a. Yes, because of SAS
b. Yes, because of ASA
c. Yes, because of SSS
d. No, because two side are congruent, no angles
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Corresponding parts
If two polygons are congruent, then their corresponding parts are congruent.
For example:
Since QRS = HGJ
That means
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Similar TrianglesTriangles are similar if:
1. All angles are congruent
2. Corresponding sides are proportional
Symbol: ABC ~ DEF
Example:
50° 50°
80°
50° 50°
80°2 62 6
5
15
A
B
C
D
E
F
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Corresponding Sides
• Sides that match
ABC ~ XBY
AC corresponds to ____
AB corresponds to _____
BY corresponds to _____ A
B
C
X Y
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Are the triangles similar?
No, ¾ is not proportional to ½
2
1
3 4
A
B
CD
E
F
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Are the triangles similar? Why or why not?
1.5
2
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If ABC ~ DEF, find x
9
11
40.5
A
B
CD
E
Fx
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Other Polygons Can Be Similar Too*They still must have congruent angles and sides must be proportional
A
B C
DE
FG
H
If the two figures are similar, what is the measure of side EH?
16
5 2
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You try!
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Which polygons are always similar?
(hint: they always have congruent angles and they will always have proportional sides)
a. Rhombuses
b. Squares
c. Triangles
d. Pentagons
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CPS Learning Series Questions!
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Problem of the Day (Thursday)If the two figures are similar, what is the
value of x?
852
71.5
x
a.11
b.5.81
c.464.75
d.14
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Right Triangles
hypotenuse
leg
leg
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Pythagorean Theorem
1. Use when you know 2 sides of a right triangle and you need to figure out the 3rd
2. a² + b² = c²3. a and b are lengths of sides and c is
the length of the hypotenuse
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Example
a²+ b² = c²a = 3, b = 43² + 4² = c²9 + 16 = c²25 = c²5 = c
3
4
x
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You try
Find the measure of
the hypotenuse x
5
12
x
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You try again!
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You also can find the length of a side
Find the missing length
a² + b² = c²8² + x² = 10²64 + x² = 100 -64
x² = 36 x = 6
x
810
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You try!
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Pam is making a new sail for her sailboat pictured below. What is the height of the
sail?
a² + b² = c²
a² + 10² = 26²
a² + 100 = 676
-100
a² = 576
a = 24
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A ladder, placed 4 ft from a wall, touches the wall 11.3 ft
above the ground. What is the approximate length of the ladder?
c2 = 42 + 11.32 Substitute.
The length of the ladder is about 12 ft.
c2 = 143.69
c2 = 16 + 127.69 Square 4 and 11.3.
Add.
Use a calculator.
Take the square root of each side.
c = 11.98708
c2 = 143.69
Draw a diagram to illustrate the problem.
c2 = a2 + b2 Use the Pythagorean Theorem.
Use the Pythagorean Theorem.
The Pythagorean Theorem
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a² + b² = c²6² + 8² = 9² ?36 + 64 = 81?100 = 81?No, she cannot use these boards
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Problem of the Day (Friday)
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You Try!
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Draw a picture!
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