Illustrative Mathematics
Illustrative Mathematics: G Gpe, G Srt Slope Criterion for Perpendicular Lines
The goal of this task is to use similar triangles to establish the slope criterion for perpendicular lines. Aligns with HSG-GPE.B.5 and HSG-SRT.B.5.
Illustrative Mathematics
Illustrative Mathematics: G Gpe, G Srt Finding Triangle Coordinates
Given a picture of a triangle on a coordinate grid, students are asked to find the coordinates of points which divide line segments in a given ratio. Aligns with G-GPE.B.6 and G-SRT.B.5.
Illustrative Mathematics
Illustrative Mathematics: G Srt Tangent Line to Two Circles
The purpose of this task is to use similar triangles and setting up a proportion in order to calculate a side length. Aligns with G-SRT.B.5.
Illustrative Mathematics
Illustrative Mathematics: G Srt Pythagorean Theorem
The purpose of this task is to prove the Pythagorean Theorem using similar triangles. Aligns with G-SRT.B.4.
Illustrative Mathematics
Illustrative Mathematics: G Srt Similar Triangles
This task works toward establishing the AA criterion for similarity of triangles. Students are asked to provide a detailed sequence of transformations that moves one of the given triangles onto the other. Aligns with G-SRT.A.3.
Illustrative Mathematics
Illustrative Mathematics: G Srt Mt. Whitney to Death Valley
In this task, learners are asked to make a mathematical model and determine if it is possible to see a point on the surface of the Earth that is 85 miles away, and well below sea level, from the top of a mountain. The curvature of the...
Illustrative Mathematics
Illustrative Mathematics: G Srt Similar Triangles
The goal of this task is to examine similarity of triangles from the point of view of proportional sides, showing that this is sufficient to conclude that two triangles are similar. Aligns with HSG-SRT.A.2.
Illustrative Mathematics
Illustrative Mathematics: G Srt Folding a Square Into Thirds
The goal of this task is to apply knowledge about similar triangles in order to understand an origami construction: trisection of the side of a square. Aligns with G-SRT.B.5.
Illustrative Mathematics
Illustrative Mathematics: G Srt Are They Similar?
In this task, students are shown two triangles that appear to be similar, but whose similarity cannot be proven without further information. Students are asked to provide a sequence of similarity transformations that maps one triangle to...
Illustrative Mathematics
Illustrative Mathematics: G Srt Joining Two Midpoints of Sides of a Triangle
In this task, students must prove that angles and triangles are congruent and that a parallel line passes through the midpoints of two sides of the larger triangle. Aligns with G-SRT.B.4.
Illustrative Mathematics
Illustrative Mathematics: G Srt Extensions, Bisections, Dissections in Rectangle
In this task, students must draw a diagram from a verbal description and use their understanding of similar triangles to find the area of a quadrilateral. Aligns with G-SRT.B.5.
Illustrative Mathematics
Illustrative Mathematics: G Mg Solar Eclipse
In this task, students investigate why total solar eclipses are rare. They will learn that, in addition to requiring the positioning of the Sun, Moon, and Earth, the Moon can only completely block out the Sun when it is closest to the...
Illustrative Mathematics
Illustrative Mathematics: 8.g, G Gpe, G Srt, G Co Is This a Rectangle?
For this task, young scholars are given four sets of coordinate pairs and are asked to determine if they represent a rectangle. Aligns with 8.G.A, 8.G.B, G-CO.B, G-GPE.B, and G-SRT.B.5.
Illustrative Mathematics
Illustrative Mathematics: 8.g, G Srt Points From Directions
For this problem, students must carefully read the description of a triangle and a fourth point that lies outside it and draw a picture to represent the problem. They must then use the Pythagorean Theorem to find side lengths. Aligns...
Illustrative Mathematics
Illustrative Mathematics: 8.ee Slopes Between Points on a Line
Eighth graders work with slopes and similar triangles in this problem and will learn why the calculated slope will be the same for any two points on a given line. Aligns with 8.EE.B.6.
Illustrative Mathematics
Illustrative Mathematics: G Srt Defining Trigonometric Ratios
The purpose of this task is to use the notion of similarity to define the sine and cosine of an acute angle. Aligns with G-SRT.C.6.
CK-12 Foundation
Ck 12: Geometry: Parallel Lines and Transversals
[Free Registration/Login may be required to access all resource tools.] Apply the fact that transversals cut parallel lines proportionally.
CK-12 Foundation
Ck 12: Geometry: Sss Similarity
[Free Registration/Login may be required to access all resource tools.] Use the SSS Similarity Theorem to determine if triangles are similar.
CK-12 Foundation
Ck 12: Geometry: Aa Similarity
[Free Registration/Login may be required to access all resource tools.] Use the AA Similarity Postulate to determine if triangles are similar.
CK-12 Foundation
Ck 12: Geometry: Right Triangle Similarity Study Guide
[Free Registration/Login may be required to access all resource tools.] An overview of altitudes and geometric mean is provided in this study guide.
Common Core Sheets
Common Core Sheets: Expressions & Equations 8.ee.6 Worksheets
Print or create worksheets to assess students' understanding of the connections between proportional relationships, lines, and linear equations.
CK-12 Foundation
Ck 12: Geometry: Aa Similarity (Intermediate)
[Free Registration/Login may be required to access all resource tools.] This concept teaches students how to identify whether or not two triangles are similar using AA Similarity.
CK-12 Foundation
Ck 12: Geometry: Sas Similarity
[Free Registration/Login may be required to access all resource tools.] This concept teaches students to decide whether or not two triangles are similar using SAS Similarity.
CK-12 Foundation
Ck 12: Geometry: Inscribed Similar Triangles
[Free Registration/Login may be required to access all resource tools.] This concept teaches students how to apply similarity to solve for missing information in inscribed right triangles.