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Resource Type
Common Core: Standard
Common Core: ELA
Common Core: Math
Subject: Geometry
255 Results

 Student Outcomes Students understand that if α and β are the measurements of complementary angles, then sin α=cos β. Students solve triangle problems using special angles.

 It is convenient, as adults, to use the notation “ ” to refer to the value of the square of the sine function. However, rushing too fast to this abbreviated notation for trigonometric functions...

 In Lesson 26, students discover that the values of the and ratios in a right triangle depend solely on the measure of the acute angle by which the adjacent, opposite, and hypotenuse sides are...

 Students link their understanding of similarity and relationships within similar right triangles formally to trigonometry. In addition to the terms sine, cosine, and tangent, students study the...

 Student Outcomes Students prove the Pythagorean Theorem using similarity. Students use similarity and the Pythagorean Theorem to find the unknown side lengths of a right triangle. Students are...

 Student Outcomes Students use the distributive property to simplify expressions that contain radicals.

 Student Outcomes Students multiply and divide expressions that contain radicals to simplify their answers. Students rationalize the denominator of a number expressed as a fraction.

 Student Outcomes Students understand that the altitude of a right triangle from the vertex of the right angle to the hypotenuse divides the triangle into two similar right triangles that are also...

 The focus in Topic D is similarity within right triangles. Students examine how an altitude drawn from the vertex of a right triangle to the hypotenuse creates two similar subtriangles. Students...

 Student Outcomes Students understand how the Greeks measured the distance from the earth to the moon and solve related problems.

 Student Outcomes Students understand that parallel lines cut transversals into proportional segments. They use ratios between corresponding line segments in different transversals and ratios within...

 Student Outcomes Students state, understand, and prove the Angle Bisector Theorem. Students use the Angle Bisector Theorem to solve problems.

 Student Outcomes Students prove the sideangleside criterion for two triangles to be similar and use it to solve triangle problems. Students prove the sidesideside criterion for two triangles to...

 Student Outcomes Students indirectly solve for measurements involving right triangles using scale factors, ratios between similar figures, and ratios within similar figures. Students use...

 Student Outcomes Students prove the angleangle criterion for two triangles to be similar and use it to solve triangle problems.

 Student Outcomes Students understand that similarity is reflexive, symmetric, and transitive. Students recognize that if two triangles are similar, there is a correspondence such that corresponding...

 Student Outcomes Students know the properties of a similarity transformation are determined by the transformations that compose the similarity transformation. Students are able to apply a similarity...

 Student Outcomes Students define a similarity transformation as the composition of basic rigid motions and dilations. Students define two figures to be similar if there is a similarity transformation...

 Students learn what it means for two figures to be similar in general, and then focus on triangles and what criteria predict that two triangles will be similar. Length relationships within and...

 In Lesson 11, students examine the effects of dilating figures from two different centers. By experimental verification, they examine the impact on the two dilations of having two different scale...

 Student Outcomes Students divide a line segment into equal pieces by the Side Splitter and Dilation Methods. Students know how to locate fractions on the number line.

 Student Outcomes Students prove that dilations map an angle to an angle with equal measure. Students understand how dilations map triangles, squares, rectangles, trapezoids, and regular polygons.

 In Grade 8, students informally showed that a dilation maps a segment to a segment on the coordinate plane. The lesson includes an opening discussion that reminds students of this fact. Next,...

 In the last lesson, students learned about the triangle side splitter theorem, which is now used to prove the dilation theorem. In Grade 8 students learned about the fundamental theorem of...