Lesson Plans SET B for Grades 7-8-Lesson 7 Level 7-8 Circles-HW

Lesson 7 Level 7-8 Circles-HW

Pdf Summary

This set of Level 7-8 homework problems focuses on the topic of circles and aims to reinforce the skills and concepts learned in a Math Kangaroo class. Here is a brief overview of the problems included and their solutions:<br /><br />1. **Problem 1**: The problem involves finding the length of DE. The given answer is 215.<br /><br />2. **Problem 2**: This involves a larger semicircle with a radius of 18 that contains two congruent smaller semicircles and a circle. The task is to determine the radius of the smaller circle, with the answer being 6.<br /><br />3. **Problem 3**: Here, the concept of geometry is applied to a circle with center O, where the diameter is the base of an isosceles triangle ABC. Points K and L are the intersections of this triangle with the circle, and given that angle ACB is 36 degrees, the problem asks for the measure of angle KOL. The solution concludes that angle KOL is 108 degrees.<br /><br />4. **Problem 4**: Involves a rectangle that contains three identical circles. Given that each circle has a radius of 1 and the base of the rectangle is 4, the height of the rectangle must be calculated. The answer, expressed in radical form, is 2√3.<br /><br />5. **Problem 5**: This problem requires finding the measure of an acute angle V in a diagram where O is the center of the circle. The answer is 31 degrees.<br /><br />These problems help solidify understanding of geometric principles related to circles, including properties of angles, triangle relations, and considerations of space and size. They also require critical thinking to apply learned concepts to solve complex configurations.

Keywords

Level 7-8 homework

circles

Math Kangaroo

geometry

semicircles

isosceles triangle

rectangle

radius

angle

critical thinking