1. To divide a line segment in a given ratio, which of the following is essential?
Answer:
Explanation:
A compass is essential to mark arcs and create points that help in dividing a line segment in a given ratio.
2. How many tangents can be drawn to a circle from an external point?
Answer:
Explanation:
Two tangents can be drawn to a circle from an external point, and they are of equal length.
3. For constructing an angle of 60°, which instrument is essential?
Answer:
Explanation:
Using a compass and straightedge, a 60° angle can be constructed as one of the basic constructible angles.
4. If the bisector of an angle divides it into two equal angles, what is the measure of each angle when the original angle is 90°?
Answer:
Explanation:
The bisector will divide the 90° angle into two equal parts, each measuring 45°.
5. To construct a triangle when its base, a base angle and the difference of the other two sides are given, you would use:
Answer:
Explanation:
Using the properties of an angle bisector, one can determine the point where the other two sides meet.
6. In the construction of a triangle, if two sides and the included angle are given, it is called:
Answer:
Explanation:
This refers to Side-Angle-Side construction of a triangle.
7. Which of the following is not a criterion for the construction of a triangle?
Answer:
Explanation:
A triangle cannot be constructed uniquely with two sides and a non-included angle.
8. To construct the perpendicular bisector of a given line segment, which instrument is necessary?
Answer:
Explanation:
A compass is essential to mark arcs from endpoints of the line segment which intersect to give points on the perpendicular bisector.
9. If in a circle with center O, a tangent at point A is drawn, which of the following is true?
Answer:
Explanation:
The radius at the point of tangency is perpendicular to the tangent, making both statements a) and c) correct.
10. To construct an angle of 15°, which other angles are needed?
Answer:
Explanation:
By subtracting a 45° angle from a 60° angle, a 15° angle can be constructed.