Polygon Vocabulary. You will be given a set of geometry cards.
With your partner group these cards in any way you want to. One table at a time will be asked to come to the board and add to a list of the properties that an be used to group the cards. In geometry the shapes are usually named using the number of sides and the types of angles. See the h t S th sheets called ll d Geometry Vocabulary Bingo Geometry terms handout Geometry terms flash cards Make a list of the vocabulary you dont know or print the sheets from the blog and use them.
Triangle Vocabulary: Triangle Names Using Sides: No equal sides: Two equal sides: Three equal sides: Scalene triangle Isosceles triangle Equilateral triangle
Triangle Names Using Angles: All angles less than 90 One angle equals 90 One angle more than 90 Acute triangle Right triangle Obtuse triangle
Give the name for the following triangles
Bisectors?
If an object is divided in half we say it has been bisected. Describe the following: A
BD bi sec ts ABC segment BD bisects angle ABC
B D
FH is the perpendicular bisector of EG
See page 413 for extra practice
Polygon Properties.
If you dont want to write all the vocabulary you can print the sheet Quadrilateral Definitions which is on the blog.
Polygons are closed figures with three or more sides.
Vocabulary: Names of polygons:
4 sides 5 sides id 6 sides 7 sides 8 sides 9 sides 10 sides
Parallelogram A quadrilateral with two pairs of parallel sides.
quadrilateral
pentagon hexagon heptagon
octagon
nonagon
decagon
Rectangle. A quadrilateral with four 900 angles.
Square. A quadrilateral with four 900 angles and four equal sides.
Rhombus. A quadrilateral with four equal sides.
Trapezoid. A quadrilateral with only one pair of parallel sides.
Kite.
A quadrilateral with two pairs of equal sides the pairs have different lengths the sides with equal lengths are next to each other.
Concave and convex Polygons
C
Concave polygons have at least one point going in.
A B
Convex polygons have all points going out
B C
Questions using properties of quadrilaterals:
See the sheet QuadrilateralComparisonChart to help with these questions.
A rectangle is a trapezoid. True or False Look at the second shape mentioned. What properties are needed for a polygon to be a trapezoid? Only one pair of parallel sides? Does a rectangle have only pair of parallel sides? No. Therefore: False because a rectangle does not have only one pair of parallel sides. OR False because a rectangle has more than one pair of parallel sides
A square is a rectangle. True or False Look at the second shape mentioned. What properties are needed for a polygon to be a rectangle? Four 900 angles? Does a square have four 900 angles? Yes. Therefore: True because a square has four 900 angles.
Is every square a rhombus. What properties are needed for a polygon to be a rhombus? A quadrilateral with four equal sides? Is a square a quadrilateral with four equal sides? Yes. Therefore: Yes because a square has four equal sides.
A parallelogram is a kite. True or False What properties are needed for a polygon to be a kite? two pairs of equal sides the pairs have different lengths the sides with equal lengths are next to each other.? Does a parallelogram have all those things? D ll l h ll th thi ? No. Therefore: False because a parallelogram does not have the equal sides next to each other.
Fill in this chart to help you practice these questions.
is always a A parallelogram square rectangle rhombus trapezoid kite
Parallel Lines Vocabulary.
F a ls e F a ls e
parallelogram
F a ls e
F a ls e
F a ls e
square
T ru e
T ru e
F a ls e
F a ls e
F a ls e
rectangle
T ru e
F a ls e
F a ls e
F a ls e
F a ls e
Corresponding Angles: Are in matching positions compared to the parallel lines and the transversal.
A and E d
G and B d
F and C d
rhombus
T ru e
F a ls e
F a ls e
F a ls e
F a ls e
Alternate Interior Angles: Are between the parallel lines and diagonally opposite.
D and F
trapezoid
E and B
F a ls e
F a ls e
F a ls e
F a ls e
F a ls e
Alternate Exterior Angles: Are outside the parallel lines and diagonally opposite.
kite
F a ls e
F a ls e
F a ls e
F a ls e
F a ls e
H and C
A and G
See the sheet geometry concepts polygons for more practice.
Parallel Lines Vocabulary.
Sum of Angles Vocabulary.
Vertical Angles: Are opposite each other on a pair of crossed lines
Supplementary Angles: Have a sum of 180
A and B
G and E
F and H
A and B
C and D
Same side interior angles: Are between the parallel lines and on the same side of the transversal.
Complementary Angles: Have a sum of 90.
D and E
F and B
B and C
Same side exterior Angles: Are outside the parallel lines and on the same side of the transversal.
A and H
G and C
Lines Concepts. Lines have no end points they extend forever in two directions.
Intersection of Lines, Segments and Rays. The intersection of two lines is? A point draw a diagram if you are unclear.
The symbol is AB. In words - line AB.
Rays have one end point they extend forever in one direction.
The symbol is AB In words - ray AB. AB. AB
Segments have two end points they have ends in two directions.
The symbol is AB. In words - segment AB.
The intersection of two rays?
Plane Concepts. Planes have no edges they extend forever in two directions.
A point or a segment draw a diagram if you are unclear.
The symbol is P. In words - plane P.
How many points are needed to exactly define a plane? Three non-collinear points define a plane.
Intersections with Planes. What is the intersection of two planes? A line draw a diagram if you are unclear
What is the intersection of a line and a plane? A line or a point draw a diagram if you are unclear.
What is the intersection of three planes? A point or a line draw diagrams or give examples using the planes in the classroom.
Intersections Summary: Fill this chart in to help you with questions such what is the intersection of a line and a segment.
Line Line Ray Segment Plane
point
ray point
segment line point point
ray point i t
Ray
ray segment segment g point i point
Segment
segment segment point point
line
Plane
For extra practice see the sheet Geometry Concept Lines and Planes
Quadrilateral summary: After doing the Geometer Sketchpad project you should be able to fill in this chart on the properties of quadrilaterals.
Parallelogram Rectangle Rhombus Isosceles Trapezoid
The sum of the angles in a triangle is 1800 The sum of the angles making up a straight line is 1800 Find the values for A and B
A B 115
Side properties
Opposite sides equal.
Adjacent pairs Adj t i sum 180 Opposite pairs are equal
Opposite sides equal.
All sides equal.
Non-parallel sides equal
Always start with something you are told and find another angle
Angle properties
All are 90
Adjacent pairs Base pairs sum 180 are equal Opposite pairs Non-base pairs are equal sum 180
32
B 115 180 B 65
The use the new angle to find another angle
Diagonal properties
Bisect each other
Bisect each other Same length
Bisect each other Bisect the angles Are perpendicular
Same length
65 A 32 180 A 83
See page 414 and sheet Triangle Questions for extra practice
For practice see the sheet GSP project: Quadrilateral and Polygon questions.
Z 110 180 z 70 xy 2x 70 180 2x 110
xy
y 32 78 180 y 110 180
y 70 x 70
2x 52 180 2x 128 x 64
Note that the angles may not be accurately drawn.
x 55
Calculations for Quadrilaterals based on the GSP project.
Parallel Lines Angle Calculations.
ABC 650 BAD 1050
length AC 14
ADC 650 length AB 20
In parallel lines a pair of angles will always be either congruent (equal) or supplementary (sum of 180)
ABC 1300 BCD 500 ADC 500 length DE 13 length M 11
length AC 20
EAB 320 0 ABE 58 BCD 640 ADC 1160 length AB 6
A and B are A and H are G and B are C and H are E and B are
congruent sup plementary congruent congruent congruent
Parallel Lines Angle Calculations.
A = 120 F = 60
Starting from the angles you are told you should be able to find every other angle. The angle may not be accurate on the diagram.
G = 120
Starting from the angles you are told you should be able to find every other angle. The angle may not be accurate on the diagram.
Similar Triangles:
1. Look at the triangle with the unknown. 2. Identify pairs of sides that have matching positions in the two triangles look at the angles to identify the positions. 3. Set up proportions with the unknown on the top.
x matches up with ? 12 4 matches up with ? 7
x 12 4 7
multiply both sides by 4
x
See page 414 and sheet Parallel Lines Questions for extra practice
48 7
See the Khan Academy video Similar Triangles
1. Look at the triangle with the unknown. 2. Identify pairs of sides that have matching positions in the two triangles look at the angles to identify the positions. 3. Set up proportions with the unknown on the top.
Calculate the sum of the angles in a polygon: Think of the polygons divided into triangle What is the connection between the number of sides and the number of triangles? The number of triangles equals =
P matches up with ? 14 6 matches up with ? 8
P 14 6 8
multiply both sides by 6
14 6 21 8 2
Each triangle equals 1800 Therefore what is the sum of all the angles in the polygon
The sum of angles in a polygon (number of sides 2) 180
Calculate the size of each interior angles in a regular polygon:
Think of the polygon divided into triangle You know how to find the sum of all the angles in the polygon Therefore how do we find the size of each interior angles in a regular polygon?
interior angle
(number of sides 2) 180 number of sides
