Illustrative Mathematics
Illustrative Mathematics: G Co Building a Tile Pattern by Reflecting Hexagons
This task applies reflections to a regular hexagon to construct a pattern of six hexagons enclosing a seventh. The focus of the task is on using the properties of reflections to deduce this seven-hexagon pattern. Aligns with G-CO.B.6.
Illustrative Mathematics
Illustrative Mathematics: G Co Building a Tile Pattern by Reflecting Octagons
This task applies reflections to a regular octagon to construct a pattern of four octagons enclosing a quadrilateral. The focus of the task is on using the properties of reflections to deduce that the quadrilateral is actually a square....
Illustrative Mathematics
Illustrative Mathematics: G Co Classifying Triangles
The goal of this task is to help students synthesize their knowledge of triangles where only two of the vertices have been given. They will need to know that a triangle inscribed in a circle, with a diameter of the circle as one side, is...
Illustrative Mathematics
Illustrative Mathematics: G Co Points Equidistant From Two Points in the Plane
In this task, students are shown a line segment that is bisected at a right angle by a second line. They are asked to prove statements about this geometric construction. Includes a GeoGebra worksheet that can be used by the instructor to...
Illustrative Mathematics
Illustrative Mathematics: G Co Midpoints of Triangle Sides
The goal of this task is to use similarity transformations to relate two triangles. The triangles are obtained by taking midpoints of two sides of a given triangle. Aligns with HSG-CO.C.10.
Illustrative Mathematics
Illustrative Mathematics: G Co Defining Perpendicular Lines
Three students have proposed three ways to describe when two lines are perpendicular. Students are asked to analyze their statements. Aligns with G-CO.A.1.
Illustrative Mathematics
Illustrative Mathematics: G Co Defining Parallel Lines
Alex and his friends are studying for a geometry test and one of the main topics covered is parallel lines. They each write down what they think it means for two distinct lines in a plane to be parallel. Learners are asked to analyze...
Illustrative Mathematics
Illustrative Mathematics: G Co Origami Equilateral Triangle
The purpose of this task is to explore reflections in the context of paper folding. Each fold is associated with a line of reflection and understanding each step in the construction requires careful analysis of angles and of the...
Illustrative Mathematics
Illustrative Mathematics: G Co Midpoints of the Sides of a Paralellogram
Suppose that ABCD is a parallelogram and that M and N are the midpoints of lines AB and CD respectively. Students are asked to prove that MN=AD, and that the line MN is parallel to line AD. Aligns with G-CO.C.11.
Illustrative Mathematics
Illustrative Mathematics: G Co Parallelograms and Translations
In this task, students apply the definition of a parallelogram in the context of a geometric construction. Aligns with G-CO.C.11.
Illustrative Mathematics
Illustrative Mathematics: G Co Reflections and Equilateral Triangles
Given an equilateral triangle, students are asked to explore its symmetries using rigid transformations of the plane. Aligns with G-CO.B.
Illustrative Mathematics
Illustrative Mathematics: G Co Showing a Triangle Congruence: The General Case
Given distinct, congruent triangles, students are asked to show that congruence can always be shown with one, two, or three rigid motions. Aligns with G-CO.A.5.
Illustrative Mathematics
Illustrative Mathematics: G Co Showing a Triangle Congruence: A Particular Case
Given two congruent triangles, students are asked to analyze the effects of different transformations. Aligns with G-CO.A.5.
Illustrative Mathematics
Illustrative Mathematics: G Co Is This a Parallelogram?
In the pictured quadrilateral, opposite sides are congruent and students must explain whether this makes it a parallelogram. Aligns with G-CO.C.11.
Illustrative Mathematics
Illustrative Mathematics: G C, G Srt Neglecting the Curvature of the Earth
Jerry and Ashley are trying to find out if it is possible to see the lowest point in the USA from the highest point in the USA. It turns out that the highest point in the United States, the peak of Mount Whitney, is only 85 miles from...
Illustrative Mathematics
Illustrative Mathematics: G Gpe, G Co, G Srt Unit Squares and Triangles
In this task, young scholars are shown three unit squares and two line segments connecting two pairs of vertices. They are asked to find the area of a triangle formed by intersecting lines. They can solve it using coordinate geometry or...
Illustrative Mathematics
Illustrative Mathematics: G C Right Triangles Inscribed in Circles I
This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle with one side of the triangle a diameter. The fact that these...
Illustrative Mathematics
Illustrative Mathematics: G C Two Wheels and a Belt
A certain machine is to contain two wheels, one of radius 3 centimeters and one of radius 5 centimeters, whose centers are attached to points 14 centimeters apart. The manufacturer of this machine needs to produce a belt that will fit...
Illustrative Mathematics
Illustrative Mathematics: G C Tangent to a Circle From a Point
This task builds on a previous one called ''Right triangles inscribed in circles I.'' Here students are asked to construct a tangent line to a circle from a point outside of the circle. Aligns with G-C.A.4.
Illustrative Mathematics
Illustrative Mathematics: G C Right Triangles Inscribed in Circles Ii
In this task, students analyze the characteristics of a right triangle that has two sides labeled with midpoints and show that the triangle is inscribed in a circle with a diameter the length of its hypotenuse. Aligns with G-C.A.2.
Illustrative Mathematics
Illustrative Mathematics: G C Locating Warehouse
You have been asked to place a warehouse so that it is an equal distance from three roads on a map. Students must fold a paper so that this point is where two folds intersect, and they must explain why their construction works and why...
Illustrative Mathematics
Illustrative Mathematics: G C Orbiting Satellite
A satellite is orbiting the Earth at a given height and students are asked to find the distance it travels to complete 70 percent of an orbit. This task provides a context for connecting an angle in radians to the arc length intercepted...
Illustrative Mathematics
Illustrative Mathematics: G Gpe.5 Triangles Inscribed in Circle
In this task, students use ideas about linear functions to determine when certain angles are right angles. They use the fact that two lines (if not vertical or horizontal) are perpendicular when their slopes are inverse reciprocals, as...
Illustrative Mathematics
Illustrative Mathematics: G C Mutually Tangent Circles
Three circles are mutually tangent. Young scholars are asked to find the total area of the circles plus the area inside where they meet. Students will need to know how to calculate the area of a circle, a sector of a circle, and an...