8th grade Math Guide

Category

ACT Readiness Standards Utah Core State Standards

G 501. Use several angle properties to find an unknown angle measure

4.MD.7. Recognize angle measure as additive 7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. 8.G.5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. SMII.G.CO.9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. SMII.G.CO.10. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. 3.MD.6. Measure area by counting unit squares (square centimeters, square meters, square inches, square feet, and improvised units) 3.MD.7. Relate are to the operation of multiplication and addition. 4.MD.3. Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. 6.G.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. 8.G.7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real -world and mathematical problems in two and three dimensions. SMII.G.SRT.7. Explain and use the relationship between sine and cosine of complementary angles. SMII.G.SRT.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems

G 506. Compute the area of triangles and rectangles when one or more additional simple steps are required

G 604. Apply basic trigonometric ratios to solve right-triangle problems

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