Lesson Plans SET A for Grades 9-10-Lesson 9 Level 9-10 2D Geometry 2

Lesson 9 Level 9-10 2D Geometry 2 - HW

Pdf Summary

The Homework Problems Level 9-10 Set A, focusing on 2D Geometry, offers a set of problems designed to enhance skills and concepts covered in Math Kangaroo classes. Here's a summary of the tasks and their solutions:<br /><br />1. **Tan 15 Degrees**: The exact value is calculated using trigonometric identities involving tan(45 - 30). The solution explores this via tan addition formulas resulting in \( \tan 15 = 2 - \sqrt{3} \).<br /><br />2. **Solving for x and y**: Given angles in a geometric figure, equations are formed using angle sum properties. Solving these, the values obtained are \( x = 6 \) and \( y = 34 \).<br /><br />3. **Measure of angle CPD in a geometric figure**: With APB as an equilateral triangle and ABCD as a square, the measure \( CPD = 150^\circ \) is deduced. It involves calculating angles by subtracting known angles in a cyclic process.<br /><br />4. **Sum of Measures of Shaded Angles**: By considering the internal angles of four triangles and subtracting total honored angle degrees, the sum of the shaded angles is concluded as 540°.<br /><br />5. **Tangent and Circle Properties**: Constructing tangents AB and AC to a circle, while CP is a parallel chord, the angle \( \angle CBP \) is calculated through a series of steps involving chord-lengths, central angles, and parallel angles, resulting in \( \angle CBP = 40^\circ \).<br /><br />Each solution employs principles from trigonometry, algebra, and geometry to solve the given problems, providing a mix of straightforward calculations and application of theoretical principles. This set is intended to hone problem-solving skills in 2D geometry, which is foundational for further studies in mathematics.

Keywords

2D Geometry

Math Kangaroo

trigonometric identities

tan 15 degrees

angle sum properties

equilateral triangle

square

cyclic process

tangent properties

problem-solving skills