Choosing Congruency Rules

Q.

If I draw a circle on a tracing paper and draw two equal chords and drop perpendicular from centre to the chord. Fold the paper such that the two chords coincide. Then, the two perpendiculars are also coinciding.

1. True

2. False

Q.

How will you prove that the construction for a triangle with the given conditions is right?

Given conditions: Base length BC is given, base angle B is given, and difference of the other two sides is given (AB-AC) where AB is greater than AC. For going about the construction, I drew the base length BC, drew the ray BX with angle XBC known to me. Taking B as centre and radius equal to (AB-AC) I cut an arc on the ray BX intersecting it at point D. I then joined D to C. Then drew the perpendicular bisector of the line segment DC and named the point of intersection of this perpendicular bisector and the ray BX as A. Joined A to C and the triangle ABC was ready

Which of the following statements gives the best explanation to this construction?

1. Since the triangles AMD and AMC are congruent, AD = AC and hence the location of A has been plotted correctly

2. the triangles DBC and CAD are congruent the location of A is justified

3. AM is the altitude for the triangle ADC and hence the location of A is justified

4. None of these

Q. Two triangles are said to be congruent by which of the following conditions?

1. One side and one angle of both the triangles are equal
2. Two sides and one non-included angle of both the triangles are equal
3. One side of both the triangles are equal
4. Two sides and one included angle of both the triangles are equal

Q.

How will you prove that the construction for a triangle with the given conditions is right?

Given conditions: Base length BC is given, base angle B is given, and difference of the other two sides is given (AB-AC) where AB is greater than AC. For going about the construction, I drew the base length BC, drew the ray BX with angle XBC known to me. Taking B as centre and radius equal to (AB-AC) I cut an arc on the ray BX intersecting it at point D. I then joined D to C. Then drew the perpendicular bisector of the line segment DC and named the point of intersection of this perpendicular bisector and the ray BX as A. Joined A to C and the triangle ABC was ready

Which of the following statements gives the best explanation to this construction?

1. None of these

2. Since the triangles AMD and AMC are congruent, AD = AC and hence the location of A has been plotted correctly

3. AM is the altitude for the triangle ADC and hence the location of A is justified

4. the triangles DBC and CAD are congruent the location of A is justified

Q.

In the following figures, are the centre of the circle and the circumcentre of the triangle the same?

1. Yes, Yes

2. No, Yes

3. Yes, No

4. No, No