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GEOMETRY
Vocabulary List
Geometry
Altitude- the perpendicular distance from the vertex to the opposite side of the
figure (base)
Face- one of the polygons of a solid figure
Diagonal- a line segment that joins two vertices of a polygon but is not a side
Polygon- a closed plane figure formed by three or more line segments
Congruent- having the same size and shape
Similar figures- figures with the same shape but not necessarily the same size
Isosceles triangle- a triangle with exactly two congruent sides
Scalene triangle- a triangle with no congruent sides
Equilateral triangle- a triangle with three congruent sides
Acute triangle- a triangle with all angles less than 90°
Right triangle- a triangle with one right angle
Obtuse triangle- a triangle with one angle greater than 90°
Reflection- a movement of a figure by flipping it over a line
Rotation- a movement of a figure by turning it around a fixed point
Translation- a movement of a figure along a straight line, only the location
changes
Dilation- a proportional shrinking or enlargement of a figure
Perpendicular lines- 2 lines that intersect to form a right (90°) angle
Parallel lines- lines in a plane that are always the same distance apart
GEOMETRY
(GRAPHIC ORGANIZER)
Using Venn Diagrams, have students show the similarities and
differences between the following shapes:
Rectangle, square and rhombus
Expand with other shapes(Two dimensional and three dimensional geometric figures)
Students can draw own Venn diagrams on paper if needed
Angle Exploration and Classification
(Hands-On Activity)
PREPARATION:
To prepare for the lesson, purchase a box of uncooked spaghetti. Cut out small triangle arrows, 6
for each student. To save time, give students a small square of construction paper to cut out the
triangle arrows. Students tape the arrows on to one end of the spaghetti pieces to make rays for
the angles.
1. Distribute three pieces of uncooked spaghetti and six small arrows to each student. Have
students break one of the spaghetti pieces into half.
2. Instruct students to make rays by taping an arrow to one end of the spaghetti. Tell students
that a ray is a line segment that has a beginning point but no end point.
3. Direct students to make an angle from the two large pieces of spaghetti. Observe the
spaghetti angles and see which direction the rays are pointing. Assist students who have the
rays pointing toward the vertex of the angle.
4. In small groups, have students share their angles. Have them compare the angle sizes and
describe them as acute, obtuse, right or straight.
5. Ask students if they can make a larger angle than the one created with the smaller spaghetti
pieces. Allow students to think about their response and turn to partner and discuss each
others response. Listen to the discussions and make anecdotal notes of the different ideas
students have. Select students having different responses to share with the class and record
on the board.
6. Ask the students:
• What determines the measure of an angle?
• What characteristic of the angle is measured?
Allow students to discuss in small groups and share responses with the class.
7. Clarify for students that the angle measure is the degree the rays are rotated from one
another. Demonstrate on the overhead by rotating spaghetti rays away from and closer to
each other. Tell students we measure angles in degrees.
8. Direct students to make a right angle with both sizes of spaghetti. Tell students that a right
angle has a measure of 90 degrees. Ask students to think about how to describe the measure
of acute, obtuse and straight angles and share with a partner.
9. Ask students to describe the measures of an acute, obtuse and straight angle. An acute angle
measures less than 90 degrees, an obtuse angle measures more than 90 degrees and a straight
angle measures 180 degrees. If students struggle with a straight angle, have them think about
going around the clock. Every three hours, the hour hand rotates 90 degrees. So how many
degrees would the hour hand move in six hours or half way around?
10. Direct students to create two angles with equal measures. Allow them to break the spaghetti
pieces into different sizes. Encourage students to describe their angles using appropriate
mathematical terms. Provide additional practice using a variety of angles with varying
degrees and ray lengths.
11. Have students reflect on their learning and record in their journal.
a. Review vocabulary by recording and defining terms such as ray, rotate and degrees.
b. Describe how to measure an angle.
c. Confirm that the lengths of the sides do not determine the angle measure.
Differentiated Instructional Support:
Instruction is differentiated according to learner needs, to help all learners either meet the intent
of the specified indicator(s) or, if the indicator is already met, to advance beyond the specified
indicator(s).
• Have six students form two angles with string overlapping, one using string four feet in
length and the other eight feet in length. One student, for each angle, represents the vertex of
the angle by holding the middle of the four-foot string or middle of the eight-foot string.
•
•
Each of the remaining four students holds the end of the strings to complete the rays of the
angle. Have students at the end of the string stand close to one another and then have one of
the students slowly walk away, increasing the size of the angle. Have students stop at various
points to have the class identify and describe the angles as an acute angle, right angle, obtuse
angle and straight angle. Students compare the two angles that are formed. At the point when
both angles are congruent, students discuss how the two angles can be congruent even if the
lengths of the sides are different.
Have students use their arms to create a 90-degree angle and then use fingers to show a 90degree angle. Show that they are the same measurement. Follow with other angle sizes for
comparison.
Have students experiment with a protractor to accurately measure angles.
Extension:
Have students draw and label angles and place them in order from greatest to the least using the
degrees of rotation.
Home Connection:
Have students complete a scavenger hunt to find various objects with angles at home. Have
students draw, label, compare and describe the angles.
Materials and Resources:
For the teacher: uncooked spaghetti, construction paper, overhead, two lengths of string
approximately three feet and six feet in length
For the student:
scissors, three full-sized pieces of uncooked spaghetti per student (two fullsized pieces and two half-sized pieces)
Adapted from:
https://ims.ode.state.oh.us/ODE/IMS/Lessons/Content/CMA_LP_S03_BD_L05_I07_01.doc
Peggy’s Pizza Parlor
(Writing Activity)
Peggy’s Pizza Parlor offers two 10-inch pizzas for the same price as the
16-inch pizza. Which is the better buy? Explain below.
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Peggy’s pepperoni special ad states that every 12-inch pepperoni pizza
has 100 pepperoni slices. If the pepperoni slices measure 1-inch across,
can the ad be true? If it is, how much of the 12-inch pizza does not have
pepperoni on it?
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GEOMETRY GAMES
Below are websites with interactive geometry games
for students to explore and play online.
http://www.apples4theteacher.com/math.html#ge
ometrygames
http://www.funbrain.com/poly/
http://www.gamequarium.com/geometry.html
http://classroom.jcschools.net/basic/mathgeom.html
http://www.aaaknow.com/geo.htm#topic18
http://www.coolmath4kids.com/geometrystuff.ht
ml
Blokus is a new game out in stores that challenges
geometric thinking. This is a great one to have in the
classroom.
1.
MINUTE DAILY REVIEW
Geometry
Circle the name of the triangle:
Equilateral
2.
Isosceles
Scalene
Are these lines parallel or perpendicular?
_____________
_____________
3.
Circle the greater number: 54 inches or 5 feet
4.
A chord is a line segment with both endpoints on the circle.
Circle: True or False
5.
V = l x w x h Circle: True OR False
6.
Two names for the line segment are __________________ and _____________.
J ____________ H
7.
A ratio is the comparison of two quantities. Circle: True OR False
8.
Is this a regular polygon?