geometry section 1-5 1112
TRANSCRIPT
Essential Questions
• How do you identify and use special pairs of angles?
• How do you identify perpendicular lines?
Sunday, September 28, 14
Vocabulary1. Adjacent Angles:
2. Linear Pair:
3. Vertical Angles:
4. Complementary Angles:
Sunday, September 28, 14
Vocabulary1. Adjacent Angles: Two angles that share a vertex and
side but no interior points
2. Linear Pair:
3. Vertical Angles:
4. Complementary Angles:
Sunday, September 28, 14
Vocabulary1. Adjacent Angles: Two angles that share a vertex and
side but no interior points
2. Linear Pair: A pair of adjacent angles where the non-shared sides are opposite rays
3. Vertical Angles:
4. Complementary Angles:
Sunday, September 28, 14
Vocabulary1. Adjacent Angles: Two angles that share a vertex and
side but no interior points
2. Linear Pair: A pair of adjacent angles where the non-shared sides are opposite rays
3. Vertical Angles: Nonadjacent angles that are formed when two lines intersect; only share a vertex
4. Complementary Angles:
Sunday, September 28, 14
Vocabulary1. Adjacent Angles: Two angles that share a vertex and
side but no interior points
2. Linear Pair: A pair of adjacent angles where the non-shared sides are opposite rays
3. Vertical Angles: Nonadjacent angles that are formed when two lines intersect; only share a vertex
4. Complementary Angles: Two angles with measures such that the sum of the angles is 90 degrees
Sunday, September 28, 14
Vocabulary5. Supplementary Angles: Two angles with measures
such that the sum of the angles is 180 degrees
6. Perpendicular:
Sunday, September 28, 14
Vocabulary5. Supplementary Angles: Two angles with measures
such that the sum of the angles is 180 degrees
6. Perpendicular: When two lines, segments, or rays intersect at a right angle
Sunday, September 28, 14
Example 1Name a pair that satisfies each condition.
a. A pair of vertical angles
b. A pair of adjacent angles
c. A linear pair
Sunday, September 28, 14
Example 1Name a pair that satisfies each condition.
a. A pair of vertical angles
∠AGF and ∠DGC
b. A pair of adjacent angles
c. A linear pair
Sunday, September 28, 14
Example 1Name a pair that satisfies each condition.
a. A pair of vertical angles
∠AGF and ∠DGC
b. A pair of adjacent angles
∠AGF and ∠FGE
c. A linear pair
Sunday, September 28, 14
Example 1Name a pair that satisfies each condition.
a. A pair of vertical angles
∠AGF and ∠DGC
b. A pair of adjacent angles
∠AGF and ∠FGE
c. A linear pair
∠AGB and ∠BGD
Sunday, September 28, 14
Example 1
d. What is the relationship between the following angles?
∠FGB and ∠BGD
Sunday, September 28, 14
Example 1
d. What is the relationship between the following angles?
∠FGB and ∠BGD
These are adjacent angles
Sunday, September 28, 14
Example 2Find answers to satisfy each condition.
a. Name two complementaryangles
b. Name two supplementaryangles
Sunday, September 28, 14
Example 2Find answers to satisfy each condition.
a. Name two complementaryangles
∠TWU and ∠UWV
b. Name two supplementaryangles
Sunday, September 28, 14
Example 2Find answers to satisfy each condition.
a. Name two complementaryangles
∠TWU and ∠UWV
b. Name two supplementaryangles
∠SWT and ∠TWV
Sunday, September 28, 14
Example 2Find answers to satisfy each condition.
c. If , find m∠RWS = 72° m∠UWV
d. If , find m∠RWS = 72° m∠RWV
Sunday, September 28, 14
Example 2Find answers to satisfy each condition.
m∠UWV = 72°
c. If , find m∠RWS = 72° m∠UWV
d. If , find m∠RWS = 72° m∠RWV
Sunday, September 28, 14
Example 2Find answers to satisfy each condition.
m∠UWV = 72°
c. If , find m∠RWS = 72° m∠UWV
(vertical angles)
d. If , find m∠RWS = 72° m∠RWV
Sunday, September 28, 14
Example 2Find answers to satisfy each condition.
m∠UWV = 72°
c. If , find m∠RWS = 72° m∠UWV
(vertical angles)
d. If , find m∠RWS = 72° m∠RWV
180° − 72°
Sunday, September 28, 14
Example 2Find answers to satisfy each condition.
m∠UWV = 72°
c. If , find m∠RWS = 72° m∠UWV
(vertical angles)
m∠RWV =108°
d. If , find m∠RWS = 72° m∠RWV
180° − 72°
Sunday, September 28, 14
Example 2Find answers to satisfy each condition.
m∠UWV = 72°
c. If , find m∠RWS = 72° m∠UWV
(vertical angles)
m∠RWV =108°
d. If , find m∠RWS = 72° m∠RWV
(supplementary angles) 180° − 72°
Sunday, September 28, 14
Example 2Find answers to satisfy each condition.
f. If , find m∠UWV = 47° m∠UWT
e. Name two perpendicular segments
Sunday, September 28, 14
Example 2Find answers to satisfy each condition.
SW and TW
f. If , find m∠UWV = 47° m∠UWT
e. Name two perpendicular segments
Sunday, September 28, 14
Example 2Find answers to satisfy each condition.
SW and TW
f. If , find m∠UWV = 47° m∠UWT
90° − 47°
e. Name two perpendicular segments
Sunday, September 28, 14
Example 2Find answers to satisfy each condition.
SW and TW
m∠UWT = 43°
f. If , find m∠UWV = 47° m∠UWT
90° − 47°
e. Name two perpendicular segments
Sunday, September 28, 14
Example 2Find answers to satisfy each condition.
SW and TW
m∠UWT = 43°
f. If , find m∠UWV = 47° m∠UWT
(complementary angles) 90° − 47°
e. Name two perpendicular segments
Sunday, September 28, 14
Example 3Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 904x + 14 = 90−14 −14
Sunday, September 28, 14
Example 3Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 904x + 14 = 90−14 −14
4x = 76
Sunday, September 28, 14
Example 3Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 904x + 14 = 90−14 −14
4x = 764 4
Sunday, September 28, 14
Example 3Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 904x + 14 = 90−14 −14
4x = 764 4x = 19
Sunday, September 28, 14
Example 3Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 904x + 14 = 90−14 −14
4x = 764 4x = 19
8y + 10 = 90
Sunday, September 28, 14
Example 3Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 904x + 14 = 90−14 −14
4x = 764 4x = 19
8y + 10 = 90−10 −10
Sunday, September 28, 14
Example 3Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 904x + 14 = 90−14 −14
4x = 764 4x = 19
8y + 10 = 90−10 −10
8y = 80
Sunday, September 28, 14
Example 3Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 904x + 14 = 90−14 −14
4x = 764 4x = 19
8y + 10 = 90−10 −10
8y = 808 8
Sunday, September 28, 14
Example 3Find x and y so that AE ⊥ CF .
2x + 14 + 2x = 904x + 14 = 90−14 −14
4x = 764 4x = 19
8y + 10 = 90−10 −10
8y = 808 8y = 10
Sunday, September 28, 14
Example 4Find the measures of two supplementary angles so that the difference between the measures of the two angles
is 44.
x° (180 − x)°
Sunday, September 28, 14
Example 4Find the measures of two supplementary angles so that the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44
Sunday, September 28, 14
Example 4Find the measures of two supplementary angles so that the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44180 − 2x = 44
Sunday, September 28, 14
Example 4Find the measures of two supplementary angles so that the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44180 − 2x = 44−180 −180
Sunday, September 28, 14
Example 4Find the measures of two supplementary angles so that the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44180 − 2x = 44−180 −180−2x = −136
Sunday, September 28, 14
Example 4Find the measures of two supplementary angles so that the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44180 − 2x = 44−180 −180−2x = −136−2 −2
Sunday, September 28, 14
Example 4Find the measures of two supplementary angles so that the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44180 − 2x = 44−180 −180−2x = −136−2 −2
x = 68°
Sunday, September 28, 14
Example 4Find the measures of two supplementary angles so that the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44180 − 2x = 44−180 −180−2x = −136−2 −2
x = 68°
180 − 68
Sunday, September 28, 14
Example 4Find the measures of two supplementary angles so that the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44180 − 2x = 44−180 −180−2x = −136−2 −2
x = 68°
180 − 68 =112°
Sunday, September 28, 14
Example 4Find the measures of two supplementary angles so that the difference between the measures of the two angles
is 44.
x° (180 − x)°
(180 − x) − x = 44180 − 2x = 44−180 −180−2x = −136−2 −2
x = 68°
180 − 68 =112°
The two angles are 68° and 112°
Sunday, September 28, 14