Similarity, Right Triangles, and Trigonometry

IMPORTANT

Mathematics Solutions from Chapter -1 - Similarity, Right Triangles, and Trigonometry

This chapter consists of topics like Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor etc.

Practice Other Topics from Similarity, Right Triangles, and Trigonometry

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor

This Chapter from Embibe Big Book for Mathematics for High School has 11 topics to practice on Similarity, Right Triangles, and Trigonometry

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides

This topic covers various concepts like Scale Factor, Similar Figures, etc.

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar

This topic covers various concepts like Symbol for Similarity of Two Triangles, AAA Criterion for Similarity of Triangles, etc.

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>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

This topic covers various concepts like Mid Point Theorem in a Triangle, Triangles on the Same Base and Same Parallels, etc.

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures

This topic covers various concepts like Notation for Congruence of Two Triangles, Congruent Figures, etc.

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles

This topic covers various concepts like Trigonometric Ratios of an Angle, Cosine of an Angle (cos A), etc.

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Explain and use the relationship between the sine and cosine of complementary angles

This topic covers various concepts like Relation between Sine and Cosecant, Relation between Tangent, Sine and Cosine, etc.

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems

This topic covers various concepts like Pythagoras Theorem, Application of Pythagorean Triplets in Geometry, etc.

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side

This topic covers various concepts like Sine Rule, Area of Triangle, etc.

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Prove the Laws of Sines and Cosines and use them to solve problems

This topic covers various concepts like Trigonometric Ratios of 90 Degree, cot(90-A), etc.

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

This topic covers various concepts like Line of Sight in Trigonometry, Measuring the Heights of Objects, etc.