Lesson Plans SET B for Grades 9-10-Lesson 8 Level 9-10- Geometry

Lesson 8 Level 9-10- Geometry - HW

Pdf Summary

The document contains a set of geometry problems related to triangles, intended as practice for students in a Math Kangaroo class. Here's a brief summary of each problem and its solution:<br /><br />1. **Problem 1**: A complex figure is formed by dividing triangle ABC into sections with some areas labeled. The task is to find the area of the shaded region. The solution involves equating areas with shared bases and heights and using the ratios of areas to deduce the area of the shaded region, which is calculated to be 10 cm².<br /><br />2. **Problem 2**: Presented are two adjacent squares with shaded triangles, and you're asked to find the area of the shaded region. By recognizing symmetry and using the area formula for triangles, the area of the blue shaded triangle is found to be 10.8 cm².<br /><br />3. **Problem 3**: A square contains an inscribed triangle with labeled areas of other triangles as 3, 4, and 5. The area of the triangle marked with a question mark is determined by setting up equations based on the areas and solving to find it is 8.<br /><br />4. **Problem 4**: A right triangle is folded, with lengths given for parts of the resulting figure. Using properties of similar triangles, the area of the shaded region is calculated using the formula for the area of a right triangle.<br /><br />5. **Problem 5**: In a trapezoid with parallel bases and intersecting diagonals, the problem requires proving a relationship involving the product of areas of the formed triangles. By using the properties of similar triangles and shared heights, the relationship S1S4 = S2S3 is proven.<br /><br />Each problem emphasizes core geometry concepts like area calculation, symmetry, similar triangles, and algebraic manipulation of equations. Students are encouraged to review their notes and recorded lessons to assist in solving these problems.

Keywords

geometry problems

triangles

Math Kangaroo

area calculation

symmetry

similar triangles

algebraic manipulation

practice problems

problem solving

student exercises