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Common Core: Math
CCLS  Math: G.SRT.4
 Category
 Similarity, Right Triangles, And Trigonometry
 SubCategory
 Prove Theorems Involving Similarity
 State Standard:
 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
15 Results

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

 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...

 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...

 Student Outcomes Students prove that a dilation maps a ray to a ray, a line to a line and a circle to a circle.

 Students study and prove the properties of dilations.

 Student Outcomes Students understand that the Ratio and Parallel Methods produce the same scale drawing and understand the proof of this fact. Students relate the equivalence of the Ratio and...

 Students revisit what scale drawings are and discover two systematic methods of how to create them using dilations. The comparison of the two methods yield the Triangle Side Splitter Theorem and the...

 Geometry Module 2: Similarity, Proof, and Trigonometry Just as rigid motions are used to define congruence in Module 1, so dilations are added to define similarity in Module 2. To be able to discuss...