SYMMETRY/
SETS
SETS
A school is designing its new logo, which will be placed on the center of the basketball court. The logo must have rotational symmetry of order 4 and also line symmetry.
If the designer chooses a regular octagon, how many lines of symmetry will it have, and what will be its order of rotational symmetry?
Rotation Symmetry = 8
Line Symmetry = 8
The general statement: "All rectangles are parallelograms" can be written in conditional form which is: _____________________
If polygons are rectangles, then they are parallelograms.
The angle formed by rays XY and XZ is written as angle __________.
∠YXZ or ∠X
In a triangle, one angle is three times as large as the smallest angle. The third angle is 20° more than the smallest angle. What are the measures of the three angles of the triangle?
Smallest angle = 32°
Second angle = 96°
Third angle = 52°
What is the fewest number of sides needed to make a polygon?
3 sides
A well-defined collection of objects is called a ____________________.
SETS
Given the statement, “All squares are rectangles.” Provide the following: Write the Conditional statement.
If polygons are squares, then they are rectangles.
In a triangle, one angle is twice the measure of the smallest angle. The third angle is 20° more than the smallest angle. Find the measures of the three angles of the triangle.
Smallest angle: 40°
Second angle: 80°
Third angle: 60°
Converse of “If a quadrilateral is a square, then it has four equal sides”
If it has four equal sides, then a quadrilateral is a square.
What is the greatest number of obtuse angles a quadrilateral can have?
2
In a survey of 60 students: 25 students like basketball (B), 20 students like volleyball (V), 18 students like soccer (S), 10 students like both basketball and volleyball, 8 students like both volleyball and soccer, 6 students like both basketball and soccer, 4 students like all three sports. How many students like only basketball?
13
Given the statement, “All squares are rectangles.” Provide the following: Write the Inverse statement.
If polygons are not squares then they are not rectangles.
A ladder is leaning against a wall. The angle between the ladder and the ground is 30° less than twice the angle between the ladder and the wall. Since the ladder touches both the ground and the wall, the two angles must be complementary. Find the measure of the angle between the ladder and the ground, and the angle between the ladder and the wall.
Angle between ladder and ground = 50°
Angle between ladder and wall = 40°
In a triangle, one angle measures 40° and another measures 65°. what is the measure of the third angle?
75°
Name all the quadrilaterals that have 4 congruent sides
rhombus and a square
In a survey of 60 students: 25 students like basketball (B), 20 students like volleyball (V), 18 students like soccer (S), 10 students like both basketball and volleyball, 8 students like both volleyball and soccer, 6 students like both basketball and soccer, 4 students like all three sports. How many students like only volleyball? ________________
6
Given the statement, “All squares are rectangles.” Provide the following: Write the Converse statement.
If they are rectangles, then the polygons are squares.
During a math contest, students are asked this challenge: “The sum of the interior angles of a polygon is 1440°." How many sides does the polygon have?
10 sides
The formula for the sum of interior angles in a polygon.
S = 180° (n - 2)
Define what a regular polygon is
A polygon is a flat figure enclosed by straight line segments that are connected through vertices.
In a survey of 60 students: 25 students like basketball (B), 20 students like volleyball (V), 18 students like soccer (S), 10 students like both basketball and volleyball, 8 students like both volleyball and soccer, 6 students like both basketball and soccer, 4 students like all three sports. How many students do not like any of the three sports? _____________________
17
Given the statement, “All squares are rectangles.” Provide the following: Write the Contrapositive statement.
If they are not rectangles, then the polygons are not squares.
During a math contest, students are asked this challenge: “The sum of the interior angles of a polygon is 1440°."If the polygon is regular, what is the measure of each interior angle?
144°
In an isosceles triangle, the vertex angle is 40°.What are the measures of the other angles?
70° and 70°
Define concave and convex polygons
A polygon with a reflex angle (concave)and has at least one interior angle greater than 180° while Convex polygon is a polygon with all angles measuring less than 180 degrees.