Download ∠ABC ∠DEF ∠GHI ∠JKL ∠ONM ∠PQR ∠TUS

SOLUTIONS
GEOMETRY & SPATIAL SENSE: CONSTRUCTING
AND
MEASURING ANGLES
Types of Angles
An acute angle is bigger than 0° and smaller than 90°.
A right angle is exactly 90°.
1. Use a protractor to measure the following angles. Complete the chart.
D
A
Angle
Measure Type
∠ ABC
48°
Acute
∠ DEF
90°
Right
∠ GHI
60°
Acute
∠ JKL
86°
Acute
∠ ONM
11°
Acute
∠ PQR
55°
Acute
∠ TUS
90°
Right
J
B
C
G
I
E
F
K
P
M
N
O
U
Q
H
L
R
T
S
DID YOU KNOW?
The worst earthquake in history happened in 1201 in the area of Egypt
and Syria. The quake killed about 1.1 million people. This was the
greatest number of deaths caused by any natural disaster in recorded
history.
Expectation: i) identify and classify acute and right angles; ii) measure and construct angles up to 90°.
Please follow your teacher’s instructions to open The Geometer’s Sketchpad and enlarge your screen.
If you need practice using the selection
, line
and point
tools, please print and complete
Introduction to The Geometer’s Sketchpad. You can find this activity at mathfrog.ca.
2.
a) Hold down the line tool and choose the ray tool.
b) Draw any angle.
3.
a) Choose the selection tool.
b) Click on empty space.
4.
a)
b)
c)
d)
e)
Select the three points one at a time. Be sure that the second point is the vertex.
Click on the Measure menu. Choose Angle.
Describe what happened. Geometer’s Sketchpad measures ∠ ABC.
Click on empty space.
Clear your screen using a selection rectangle and the delete key.
5.
a)
b)
c)
d)
e)
f)
g)
Choose the ray tool and draw any two acute angles.
Choose the selection tool.
Click on empty space.
Measure one angle. The size of ∠ DEF is °. Answers will be
Click on empty space.
between 0° and 90°
Measure the other angle. The size of ∠ GHI is °.
Clear your screen using selection rectangles and the delete key.
6.
a)
b)
c)
d)
Draw two angles that appear to be right angles.
Measure each angle.
∠ PQR = °
∠ STU = ° Answers should be close to
Clear your screen.
90°
7.
a)
b)
c)
d)
Choose the ray tool and draw any angles which are larger than 90°.
Measure each angle.
∠ JKL = °
∠ MNO = ° Answers will be between
Clear your screen.
90° and 180°
TRY THIS!
Click on the File menu. Choose New Sketch. Hold down the ray tool and choose
the line segment tool.
Construct any triangle. Click on empty
space. Measure the three angles. The sum of the three angles is 180°. Drag
(move) one of the corner points (vertices). The sum of the three angles of the new
triangle is 180°. Drag one of the sides. The sum of the angles in the triangle is
180°. What appears to be the sum of the angles of any triangle? 180°
Repeat this process for any quadrilateral (4-sided figure). What appears to be the
sum of the angles of any quadrilateral? 360°
Expectation: i) identify and classify acute and right angles; ii) measure and construct angles up to 90°.