Download Lesson 3 - Constructing Angles and Triangles Notes:HW

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Lesson 3 - Constructing Angles and Triangles
Use a protractor to measure the following angles.
Steps:
1. Extend one side of the angle using your straight edge or ruler.
2. Place your protractor so that the vertex is in the origin (center of the protractor) and the
bottom line of the protractor matches with the bottom line of the angle so that it lines up at 0°.
3. Read the protractor and if the angle is small (acute), read the small numbers; if the angle is
big (obtuse), read the higher numbers; if the angle is a right angle, it should line up to 90°.
4. Draw your angle mark and label the angle.
Example 1:! !
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Example 2:
Use a protractor to construct the following angles.
Steps:
1. First draw a line segment using a straight edge or ruler.
2. Choose one of the vertices to draw the angle.
3. Place your protractor so that the vertex is in the origin (center of the protractor) and the
bottom line of the protractor matches with the bottom line of the angle so that it lines up at 0°.
4. Determine whether the angle is an acute, right, obtuse angle. Find the number of the angle
given. Make a tick mark above the number given.
5. Use the straight edge or ruler to connect the vertex to the tick mark. Draw arrows at the end
of each line you created.
6. Label the angle.
Example 3: ! m∠A = 65°! !
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Example 4: m∠ABC = 104°
Use a protractor to construct the following triangles
If you are given three angles of a triangle
STEPS:
1. First draw a line segment of any length.
2. To measure the first angle place your protractor so that the one of the vertices is in the origin
(center of the protractor) and the bottom line of the protractor matches with the bottom line of
the angle so that it lines up at 0°.
3. Find the first measurement (smallest angle) on your protractor by making a tick mark where
the angle is on the outside of the protractor and then use the straight edge to connect the
vertex to the tick mark to create the line.
4. Now repeat steps 2 and 3 with the other vertex and create the second angle.
5. Measure the last angle to check your work. Label your vertices and angles given.
Example 5:
Given the △CAR, where m∠C = 60°, m∠A = 45°, and m∠R = 75°, draw a triangle.
You Try:
5. Given the △TRI, where m∠T = 40°, m∠R = 30°, and m∠I = 110°, draw a triangle.
If you are given two angles and one side that is in between the angles of a triangle
STEPS:
1. First draw the side length given.
2. To measure the first angle place your protractor so that the one of the vertices is in the origin
(center of the protractor) and the bottom line of the protractor matches with the bottom line of
the angle so that it lines up at 0°.
3. Find the first measurement given on your protractor and then make a tick mark where the
angle is on the outside of the protractor and then use the straight edge to connect the vertex
to the tick mark to create the line.
4. Now repeat steps 2 and 3 with the other vertex and create the second angle given. You
should have an angle drawn on both sides of your side length given.
5. Label your vertices, side length, and angles given.
Example 6:
Given the △RED, where ED = 3 cm, m∠RED = 65°, and m∠EDR = 50°, draw a
triangle.
You Try:
6. Given the △EAT, where EA = 4 cm, m∠ TEA = 74°, and m∠EAT = 26°, draw a
triangle.
If you are given two sides and one angle that is included in between the sides of a
triangle
STEPS:
1. First draw the first side length given.
2. To measure the given angle place your protractor on the vertex of the angle given so that the
one of the vertices is in the origin (center of the protractor) and the bottom line of the
protractor matches with the bottom line of the angle so that it lines up at 0°.
3. Find the first measurement given on your protractor and then make a tick mark where the
angle is on the outside of the protractor and then use the straight edge to connect the vertex
to the tick mark to create the line. The length of this side length should be the length of the
second side length given.
4. Connect both the side lengths given to create the third side of the triangle.
5. Label your vertices, side lengths and angle given.
Example 7:
Given the △BAT, where BT = 4 cm, AT = 6 cm and m∠BTA = 125°; draw a triangle.
You Try:
7. Given the △SKY, where YS = 5 cm, YK = 3 cm and m∠SYK = 115°; draw a
triangle.
If you are given one side and one angle
STEPS:
1. First draw the side length given.
2. To measure the given angle place your protractor so that the one of the vertices is in the
origin (center of the protractor) and the bottom line of the protractor matches with the bottom
line of the angle so that it lines up at 0°.
3. Find the first measurement given on your protractor and then make a tick mark where the
angle is on the outside of the protractor and then use the straight edge to connect the vertex
to the tick mark to create the line.
4. Connect both the side lengths given to create the third side of the triangle.
5. Label your vertices, side length and angle given.
Example 8:
Given △HMS, where m∠M = 130° and MS = 2 cm; draw a triangle.
You Try:
8. Given △CUB, where ∠CBU = 55° and CB = 6 cm; draw a triangle.
If you are given two angles and one side that is NOT included in between the angles of a
triangle
STEPS:
1. First draw a line segment of any length.
2. To measure the first angle place your protractor so that the one of the vertices is in the origin
(center of the protractor) and the bottom line of the protractor matches with the bottom line of
the angle so that it lines up at 0°.
3. Find the first measurement given on your protractor by determining if it is an acute, obtuse, or
right angle and then make a tick mark where the angle is on the outside of the protractor and
then use the straight edge to connect the vertex to the tick mark to create the line.
4. Now repeat steps 2 and 3 with the other vertex and create the second angle given. You
should have an angle drawn on both sides of your side length given. But this time the side
length should be the side length given.
5. Label your vertices, side length, and angles given.
Example 9:
Given △XYZ, where m∠ZXY = 40°, m∠XYZ = 80°, and YZ = 4 cm; draw a triangle.
You Try:
9. Given △SOX, where m∠XOS = 25°, m∠OSX = 105°, and SX = 3 cm; draw a
triangle.