Geometry and Measurement
Two angles are complementary. If the measure of one of the angles is 68°, what is the measure of the other angle?
22° because the sum of the measures of complementary angles is 90°.
Marvin is trying to get to his friend's house. He walks 4 blocks north to the park, then turns right and walks 3 blocks. Finally he turns right and walks 4 blocks. How far from his starting point does he wind up?
3 blocks east
What is the volume of an ice cream cone that is 6cm wide at the top and 12cm tall?
36π cm3 The volume of a cone is equal to ⅓ × π × r2 × h. Since the diameter of the base of the cone is 6 cm, the radius of the base of the cone is 3 cm. Therefore the volume of the cone is equal to ⅓ × π × 32 × 12, which equals 36π cm3.
There are 9 regular parallelograms that compose a single large one. If the perimeter of each of the regular parallelograms is 14, what is the perimeter of the large figure?
42 If the perimeter is 14 then each side is 3.5 (14 ÷ 4 = 3.5). There are 12 sides used to compose the larger parallelogram. 12 × 3.5 = 42
Rigid Transformation
A geometric transformation after which the image and pre-image are congruent (length and angle measure are preserved).
Translation / Slide
A geometric transformation consisting of a movement to the right or left, up or down, or a combination of movements.
Rotation / Turn
A geometric transformation consisting of a turn of a shape about a point, often the origin, (0, 0)
Glide Reflection
A geometric transformation consisting of two transformations at once: a translation and a reflection
Reflection / Flip
A geometric transformation over a line that that produces a mirror image of the original object or image
Proof
A new true statement using multiple axioms and theorems.
Tessellation
A pattern of shapes that fit perfectly together
a convex pentagon
A pentagon has 5 sides. A convex polygon has no angles greater than 180°. Another way to think of how to identify a convex pentagon is that it has no angles pointing inward.
Coordinate Plane
A plane, often divided into a grid, with a horizontal x-axis and a vertical y-axis that intersect at the origin
Regular Polygon
A polygon with all sides congruent to each other and all angle measures congruent to each other
Irregular Polygon
A polygon with sides and angle measures that are not all the same
Equilateral Triangle / Equiangular Triangle
A regular polygon of three sides; triangle with all sides congruent to each other and all angles congruent to each other.
Symmetric
A shape that can be split into at least one pair of mirror images.
Asymmetric
A shape that can not be split into at least one pair of mirror images.
Theorem
A statement that is accepted because it has been proven
Mr. King gives his students this figure and asks students to determine its perimeter. About 80% of the students give the correct response, but he receives several responses of 100. How should he address the issue?
During group work, pull aside the students who go the answer incorrect and review the difference between perimeter and area.
Mr. Marlowe wants his students to be able to interpret word problems relating to geometry. He has many ELL students. What is the best way to clarify the meaning of various prepositions such as: above, below, together, apart, inside, etc.?
Give students a visual diagram that explains these terms.
Mrs. Blue wants her students to be able to write two column geometric proofs. Which is the most appropriate way to determine their mastery?
Give students an open ended exam where they write multiple two column proofs.
In which quadrant is the point (-5, -3) located?
III Points with negative x and y coordinates are located in quadrant III.
Eddie graphs the point (-4, -8) on the coordinate plane. Which quadrant is the point in?
III Since both coordinate values are negative, (-4, -8) is in the third quadrant.
Corresponding Angles
If a transversal intersects two parallel lines, the pairs of corresponding angles are congruent.
Alternate exterior angles
If a transversal intersects two parallel lines, then the alternate exterior angles are congruent.
Alternate interior angles
If a transversal intersects two parallel lines, then the alternate interior angles are congruent.
Volume
The measure of the total three-dimensional space contained inside an object
Vertical Angles
The pair of opposite angles created when two lines (or line segments) intersect. The angles are congruent (equal).
Origin
The point of intersection of the x-axis and y-axis of a coordinate plane, often designated as (0,0)
Circle
The set of all points equidistant (the same distance) from a given point (the center). Circles have no sides nor interior angles.
Point
a location in space without any dimension
Polygon
a multi-sided, closed figure made up of vertices (corners) and edges (sides)
There is a line AB defined by two points A and B. If Carly draws a point M that is not on line AB, which geometric figure is defined by the point M and the line?
a plane
Vertex
a point where two rays, lines, or line segments meet, such as the point where two rays, lines, or line segments intersect to form an angle
Right Prism
a prism that has the two bases aligned with each other vertically, creating sides that are perpendicular to the bases (meet the bases at right angles), creating rectangular faces
Oblique Prism
a prism with bases that are not exactly above/below each other, creating faces that are parallelograms (without right angles)
Which of the following terms would be used to describe a polygon with six sides whose angles are all of equal measure?
a regular hexagon Since all angles are of equal measure, the polygon is regular. Since it has six sides it is a hexagon.
Pyramid
a shape in three dimensions that has a polygon for a base and triangular faces that meet at a point (the apex)
Prism
a three-dimensional figure with quadrilateral faces with two congruent bases (and no apex)
Axiom / Postulate
a truth that is accepted as being self-evident, without proof
Net
a two-dimensional representation or pattern for a three-dimensional object
Acute Angle
an angle measuring between 0° and 90°
Reflex angle
an angle measuring between 180° and 360°
Obtuse angle
an angle measuring between 90° and 180°
Straight angle
an angle measuring exactly 180°
Plane
an infinite "surface" with no thickness that extends infinitely in all directions
Line
an infinite set of points arranged "straight" in opposing directions, with infinite length and no thickness
Congruent Shapes
equal in measure, symbolized by ≅
Collinear
lying on the same line
Coplanar
lying on the same plane
Convex Polygon
polygon for which all interior angles are less than 180⁰; vertices seem to point outward; all diagonals will be contained within the polygon
Concave Polygon
polygon that has at least one interior angle that is more than 180⁰; at least one vertex seems to point inward; diagonals pass outside of the polygon
Equiangular Polygon
polygon with all angles congruent (equal measure)
Equilateral Polygon
polygon with all sides congruent (equal length)
Quadrilateral
polygon with four vertices and four sides
Triangle
polygon with three vertices and three sides
Sphere
set of points in 3-dimensional space that are all the same distance from a given point (the center) Ball
Similar Shapes
shapes are similar when they have congruent angle measures and number of sides, but different overall size
Area
the amount of surface inside of a figure
Vertices
the corners of the shape
Perimeter
the distance around the outside of a figure
Slant height
the distance from the apex (top) to an edge of the base
Radius of a Circle
the distance from the center of a circle to a point on the circle
Angle
the figure formed by the intersection of two rays, lines, or line segments, or else by two rays with a common endpoint
Diameter of a Circle
the length of a segment that goes from one point on a circle through its center, and continues on to another point on the other side of the circle
Circumference
the perimeter of a circle
Face
the sides of the shape
Right Triangle
triangle with one right angle measuring exactly 90⁰
Which three dimensional figure has 6 vertices, 9 edges, and 5 faces?
triangular prism
Supplementary Angles
two angles that sum to 180°
Complementary angles
two angles that sum to 90°
Edge
where these faces meet
Total Surface Area
The sum of all of the areas of all faces of a solid object For a soup can, the area of the curved part plus the areas of the top and base
Lateral Surface Area
The sum of the areas of all faces excluding the base(s) of a solid object
Isosceles Triangle
Triangle with (at least) two sides congruent to each other and their two base angles congruent to each other.
Acute Triangle
Triangle with each angle being an acute angle; each angle measuring less than 90⁰
Scalene Triangle
Triangle with no sides or angles congruent to each other. All three sides are of different lengths.
Obtuse Triangle
Triangle with one obtuse angle; one angle measuring more than 90⁰
Juan is 5 feet tall and casts a shadow that is 10 feet long. If the flagpole casts a shadow that is 30 feet long, how tall is the flagpole?
15 feet Since Juan and the flagpole are in the same setting, they are creating similar shapes. A proportion can be used. Juan is 5 feet tall and casts a 10 foot shadow, while the unknown height flagpole casts a 30 foot shadow.
Mrs. Perkins is beginning to teach her class about congruent shapes. Which of the activities below is the best activity to introduce the subject?
Allow students to use cutouts of shapes that have been magnified to different dilations and compare and contrast their attributes.
Right Angle
An angle measuring exactly 90°, such as the corner of a piece of paper. All right angles are congruent
Ms. Nakaroti wants to teach her students about properties of points, lines, planes, and angles. Which of the following should she include in her planning for the unit?
Analyze the standards to determine learning objectives before she starts writing lesson plans.
Surface Area
The area of the outside surface of a three-dimensional object
Spatial Reasoning
The ability to think about how things appear in real life, often by use of a drawing.
Perpendicular Lines
Lines that intersect at a right (90º) angle. They have slopes that are opposite reciprocals, meaning their signs (positive or negative) are opposite and their fractions are flipped.
Parallel Lines
Lines that never intersect (coplanar). They have slopes that are congruent.
Ms. Trask wants to create an authentic assessment to test her students about angles in triangles. Which of the following should she do first?
Look at the standards to determine what a meaningful task that students could complete to demonstrate their knowledge.
Ms. Todd gives students a project where she gives all students in her class a single set of ordered pairs numbered 1 through 30. They need to graph ordered pairs in order and then connect the dots in the order in which they are graphed to make a picture. This serves as their final unit project on graphing points on the coordinate plane. Is this a suitable project?
No, because students can easily copy each others work.
Quadrant
One of the 4 areas bounded by the x-axis and y-axis of a coordinate plane
Linear Equation: Slope-Intercept Form
One way to write a linear equation (y = mx + b) where the product of the slope (m) and the variable (x) are added to the y-intercept (b) y = mx + by=mx+b
Rhombus
Parallelogram with all sides of congruent length.
Rectangle
Parallelogram with four right (90°) angles. Both pairs of opposite sides are parallel. Sides do NOT need to be congruent, but can be.
Mr. Macrow's first-grade class is having a hard time understanding prepositions for directionality. What is the most effective lesson for his students?
Provide an anchor chart and objects. Have students move two objects to form each relationship on the chart.
Trapezoid
Quadrilateral with one pair of parallel sides and one pair of non-parallel sides
Parallelogram
Quadrilateral with two pairs of opposite sides that are parallel to each other
Square
Rectangle with four congruent sides (four sides of the same measure)
A two-dimensional net of a three-dimensional figure has 5 faces, 8 edges, and 5 vertices. What figure is represented by the net
Rectangular Pyramid
Ordered Pairs
Representations in the form (x, y) of points in the coordinate plane
Which of the following terms best describes a polygon with 4 sides whose angles are all of equal measure?
Square
