Help with this questions? ### Educational Geometry Problems1. **Compass and Straightedge Construction**: - **Problem Statement**: On a given line $ l $, use only a compass and straightedge to construct the point that is equidistant to the points $ A $ and $ B $ that are not on $ l $. Explain why the point is as required. - **Diagram**: Shows points $ A $ and $ B $ on opposite sides of line $ l $.2. **Quadrilateral Intersection**: - **Problem Statement**: In a quadrilateral $ ABCD $, segment $ AB $ is congruent to segment $ BC $, and segment $ CD $ is congruent to segment $ DA $. Show that $ BD $ and $ AC $ intersect at a right angle.3. **Triangle Perpendicular Bisectors**: - **Problem Statement**: Show that the perpendicular bisectors of the three sides of a triangle meet at one point. (Hint: Use the fact that the points on the perpendicular bisector of a line segment are equidistant from the endpoints of the line segment).4. **Inscribing Squares in Isosceles Right Triangles**: - **Problem Statement**: There are two ways to inscribe a square into an isosceles right triangle. See the figures below. Find the ratio of the area of the square in the figure on the left to the area of the square in the figure on the right if the two isosceles triangles are congruent. - **Diagrams**: - **Left Figure**: Shows an isosceles right triangle with a square inscribed such that it touches two sides of the triangle. - **Right Figure**: Shows an isosceles right triangle with a different configuration of an inscribed square, which is partitioned into smaller triangles and squares.The diagrams illustrate geometric methods and comparisons of areas in different configurations of inscribed shapes.

Name: Help with this questions? ### Educational Geometry Problems1. **Compas
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Description: Help with this questions? ### Educational Geometry Problems1. **Compass and Straightedge Construction**: - **Problem Statement**: On a given line $ l $, use only a compass and straightedge to construct the point that is equidistant to the points

Fix the compass to more than half of the distance between A and B.Draw a circle centered at A using the compass:Draw a circle centered at B without changing the measurement of the compass:Mark the point of intersection of the two circles:Choose the one of the point M from the two which is not in the line I. The point lies in the both circle. Result: The points on the circle is equidistant with it's center. The point M is equidistant with both A and B.

Answered: 1. On a given line / use only compass…

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1. On a given line / use only compass and straightedge to construct the point that is equidistant to the points A and B that are not on I. Explain why the point is as required. A B

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Help with this questions?

### Educational Geometry Problems

1. **Compass and Straightedge Construction**:
- **Problem Statement**: On a given line $ l $, use only a compass and straightedge to construct the point that is equidistant to the points $ A $ and $ B $ that are not on $ l $. Explain why the point is as required.
- **Diagram**: Shows points $ A $ and $ B $ on opposite sides of line $ l $.

2. **Quadrilateral Intersection**:
- **Problem Statement**: In a quadrilateral $ ABCD $, segment $ AB $ is congruent to segment $ BC $, and segment $ CD $ is congruent to segment $ DA $. Show that $ BD $ and $ AC $ intersect at a right angle.

3. **Triangle Perpendicular Bisectors**:
- **Problem Statement**: Show that the perpendicular bisectors of the three sides of a triangle meet at one point. (Hint: Use the fact that the points on the perpendicular bisector of a line segment are equidistant from the endpoints of the line segment).

4. **Inscribing Squares in Isosceles Right Triangles**:
- **Problem Statement**: There are two ways to inscribe a square into an isosceles right triangle. See the figures below. Find the ratio of the area of the square in the figure on the left to the area of the square in the figure on the right if the two isosceles triangles are congruent.
- **Diagrams**:
- **Left Figure**: Shows an isosceles right triangle with a square inscribed such that it touches two sides of the triangle.
- **Right Figure**: Shows an isosceles right triangle with a different configuration of an inscribed square, which is partitioned into smaller triangles and squares.

The diagrams illustrate geometric methods and comparisons of areas in different configurations of inscribed shapes.

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