Jan 26, 2016 - 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.
Jan 26, 2016 - 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...
Jan 26, 2016 - 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...
Jan 26, 2016 - 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...
Jan 26, 2016 - 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...
Jan 26, 2016 - 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.
Jan 26, 2016 - 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...
Jan 26, 2016 - 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 sub-triangles. Students...
Jan 26, 2016 - 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...
Jan 26, 2016 - Student Outcomes
Students state, understand, and prove the Angle Bisector Theorem.
Students use the Angle Bisector Theorem to solve problems.
Jan 26, 2016 - Student Outcomes
Students prove the side-angle-side criterion for two triangles to be similar and use it to solve triangle problems.
Students prove the side-side-side criterion for two triangles to...
Jan 26, 2016 - Student Outcomes
Students indirectly solve for measurements involving right triangles using scale factors, ratios between similar figures, and ratios within similar figures.
Students use...
Jan 26, 2016 - 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...
Jan 26, 2016 - 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...
Jan 26, 2016 - 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...
Jan 26, 2016 - 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...
Jan 26, 2016 - 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...
Jan 26, 2016 - 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.
Jan 26, 2016 - 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.
Jan 26, 2016 - 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,...
Jan 26, 2016 - 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...
