Download Vertex of an angle

Geometry Notes
1.4 Measure and Classify Angles
Name:_________________________
Period:_______Date:_____________
Ray:
Part of a line that consists of a point called an endpoint and all points on the line that extend in one
direction.
Angle:
Consists of two different rays with the same endpoint. The rays are the sides of the angle, and the
endpoint is the vertex of the angle.
Vertex of an angle:
Is the point where two rays begin or meet, where two line segments join or meet, where two lines
intersect (cross), or any appropriate combination of rays, segments and lines that result in two straight
"sides" meeting at one place.
1. Name the vertex of the angle.
Name the sides of the angle.
Name the angle in 4 ways.
Angles are measured in degrees between 0° and 180° . What does a 0° angle look like? What would a
180° angle look like?
2. Use a protractor to measure the following angles. (place the small home over the vertex.
Angles can be classified as the following:
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Geometry Notes
1.4 Measure and Classify Angles
Name:_________________________
Period:_______Date:_____________
Acute Angle:
An angle with measure between 0° and 90° .
Right Angle:
An angle with measure equal to 90° .
Obtuse Angle:
An angle with measure between 90° and 180° .
Straight Angle:
An angle with measure equal to 180° .
3. Measure and classify each angle.
a. ∠𝐽𝐻𝐾
b. ∠𝐺𝐻𝐾
c. ∠𝐺𝐻𝐽
d. ∠𝐺𝐻𝐿
Angle Addition Postulate:
If 𝑃 is in the interior of ∠𝑅𝑆𝑇 then 𝑚∠𝑅𝑆𝑇 = 𝑚∠𝑅𝑆𝑃 + 𝑚∠𝑃𝑆𝑇.
4. 𝑚∠𝑄𝑅𝑃 = 45° , and 𝑚∠𝑄𝑅𝑁 = 132° , find 𝑚∠𝑃𝑅𝑁 and 𝑚∠𝑀𝑅𝑁.
5. Suppose 𝑚∠𝐵𝐴𝐶 = 137° . Find 𝑥 and 𝑚∠𝐵𝐴𝐷.
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Geometry Notes
1.4 Measure and Classify Angles
Name:_________________________
Period:_______Date:_____________
Find the value of 𝑥.
6.
7.
8.
9.
Congruent Angles:
Angles that have the same measure.
ACTIVITY:
1.
2.
3.
4.
Use a ruler to draw and label an acute angle. ∠𝐴𝐵𝐶
Fold the paper so that BC is on top of BA.
Draw a point D on the fold inside ∠𝐴𝐵𝐶.
Measure ∠𝐴𝐵𝐶, ∠𝐴𝐵𝐷, and ∠𝐷𝐵𝐶. What do you observe?
Angle Bisector:
A ray that divides an angle into two angles that are congruent.
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Geometry Notes
1.4 Measure and Classify Angles
Name:_________________________
Period:_______Date:_____________
In the diagram, YW bisects ∠𝑋𝑌𝑍 and 𝑚∠𝑋𝑌𝑊 = 18° . Find 𝑚∠𝑋𝑌𝑍.
10.
Be careful when you look at a geometric figure. Don’t make assumptions!
You MAY assume
 Things that look straight are straight


Points of intersection are accurate
Points shown on a line are collinear
You MAY NOT assume (unless marked)
 Exact measurements and sizes of figures
(right angles)
 Parallel and Perpendicular lines
 Shapes are congruent
a. Is ̅̅̅̅
𝐹𝐶 ≅ ̅̅̅̅
𝐹𝐸 ?
b. Are C, D, and E collinear?
c. Is ̅̅̅̅
𝐹𝐷 ⊥ ̅̅̅̅
𝐶𝐸?
Homework Assignment
1.4 Page 28
1, 3, 4, 6-17 all, 21-27 all, 29-31 all, 40, 41, 48, 51, 52
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