Grade 7 Mathematics Workbook Page 72 Bright Horizon provides guidance on solving exercises 1, 2, 3 of Properties of three perpendicular bisectors of a triangle. Students can refer to easily solve homework exercises in the textbook, grasp the solving methods, and improve results in tests and exams.
Other good Grade 7 Mathematics resources include:
- Grade 7 Mathematics Bright Horizon Workbook
- Grade 7 Mathematics Page 115 Workbook Volume 2 Sky Kite - Exercise 12. Properties of three perpendicular bisectors of a triangle
- Grade 7 Mathematics Page 81 Workbook Volume 2 Knowledge Connection - Exercise 35: Concurrency of three perpendicular bisectors, three altitudes in a triangle
Grade 7 Mathematics Page 72 Textbook Workbook Volume 2 Bright Horizon
1. Solving Exercise 1 Page 72 Mathematics Grade 7 Textbook
Problem Statement: Draw three acute, right, obtuse triangles.
a) Determine point O equidistant from the three vertices of each triangle.
b) Provide your comments on the position of point O in each case.
Solution:
The three perpendicular bisectors of a triangle intersect at a single point. This point is equidistant from the three vertices of the triangle.
Answer:
a)
b)
If the triangle is an isosceles triangle, point O is the midpoint of the hypotenuse.
If the triangle is an acute triangle, point O lies inside the triangle.
If the triangle is an obtuse triangle, point O lies outside the triangle.
2. Solving Exercise 2 Page 72 Mathematics Grade 7 Textbook
Problem Statement: Given acute triangle ABC. Let M, N, P be the midpoints of the sides AB, BC, CA respectively, and let O be the point equidistant from the three vertices of triangle ABC. Prove that MO is perpendicular to AB, NO is perpendicular to BC, and PO is perpendicular to AC.
Solution:
The three perpendicular bisectors of a triangle intersect at a single point. This point is equidistant from the three vertices of the triangle.
Answer:
Since O is the point equidistant from the three vertices of the triangle, O is the intersection of the three perpendicular bisectors.
As M, N, P are the midpoints of the sides AB, BC, CA respectively, OM, ON, OP are the perpendicular bisectors of the segments AB, BC, AC respectively.
Therefore, MO is perpendicular to AB, NO is perpendicular to BC, and PO is perpendicular to AC.
3. Solving Exercise 3 Page 72 Mathematics Grade 7 Textbook
Problem Statement: One wants to restore a broken ancient disk, which is circular and only one piece remains (Figure 6). How can you determine the radius of this ancient disk?
Solution:
Use the properties of the perpendicular bisectors of a triangle to find the center and radius of the disk.
Answer:
On the outer edge is the remaining circular path of the disk where we mark three arbitrary points A, B, C.
To determine the radius of the disk, we first need to locate its center by drawing the perpendicular bisectors of the line segments AB and BC intersecting each other at point O. Point O is the center, and OA, OB, OC are the radii of the circle.
Then, the length of segment OA is the radius of the disk.
Here is the guide for solving math problems for 7th grade page 72 workbook 2. Students can refer to solving math problems for 7th grade page 75, 76 workbook 2 beforehand and review solving math problems for 7th grade page 70 workbook 2 to ensure understanding.
- Solving Math Problems for 7th Grade Page 75, 76 Workbook 2 of Bright Horizon - Exercise 7: Properties of the three medians of a triangle
- Solving Math Problems for 7th Grade Page 70 Workbook 2 of Bright Horizon - Exercise 5: Perpendicular bisector of a line segment
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