Test Session Unit#11: Loci and Construction (9th Mathematics)

Q1. Choose the correct option. (10 × 1 = 10 marks)

1. What is the point of concurrency of the perpendicular bisector of a triangle called? Geometry

(A) Centroid (B) Orthocenter (C) Circumcenter (D) Incenter

2. In a triangle, the medians intersect at a point called:

(A) Centroid (B) Orthocenter (C) Circumcenter (D) Incenter

3. Which of the following measurements can form a triangle?

(A) 1cm, 2cm, 4cm (B) 2cm, 3cm, 6cm (C) 3cm, 4cm, 8cm (D) 5cm, 6cm, 7cm

4. Which of the following is not a criteria for triangle congruence? Congruence

(A) SSS (B) SAS (C) AAA (D) ASA

5. The centroid of a triangle divides each median in the ratio:

(A) 1:1 (B) 1:2 (C) 2:1 (D) 3:1

6. In a triangle, the angle bisector divides the opposite side in the ratio of:

(A) Adjacent sides (B) Opposite sides (C) The angles (D) The medians

7. The orthocenter of a right triangle is at:

(A) The midpoint of the hypotenuse (B) Orthocenter (C) The vertex of the right angle (D) The circumcenter

8. The orthocenter of an acute triangle lies:

(A) Outside the triangle (B) On the hypotenuse (C) Inside the triangle (D) At the centroid

9. The line segment joining the midpoint of a side to its opposite vertex in a triangle is called:

(A) Median (B) Perpendicular bisector (C) Angle bisector (D) Circle

10. The angle bisectors of a triangle intersect at ……

(A) One point (B) Two points (C) Three points (D) Four points

Q2. Write down short answers of following questions. (15 × 2 = 30 marks)

1Define the term “Loci”. Write its importance.

2Define Isosceles Triangle. Also give example.

3State Triangle Inequality Theorem. Also give example.

4When does the Ambiguous Case (SSA) occur? Give example.

5Define Perpendicular Bisector of a triangle. Also give example.

6Define Median of a triangle. Also give example.

7What is Point of Concurrency?

8Define Altitudes of a triangle. Also give example.

9Define Orthocenter of a triangle. Also give example.

10Construct a triangle of sides 5.3cm, 5.9cm and 6.2cm. (Example 1)

Describe your construction steps in the space below

11Construct a triangle BCD in which measures of two sides are 5.5cm and 4.2cm and measure of their included angle is 60°. (Example 2)

Describe your construction steps in the space below

12Draw a triangle CDE when \( mDE = 4.3cm \), \( m\angle D = 30^\circ \) and \( m\angle E = 120^\circ \). (Example 3)

Describe your construction steps in the space below

13Construct triangles DEF and D’E’F’ when \( mDE = 6cm \), \( m\angle D = 30^\circ \) and \( mEF = 3.6cm \) (Example 5 – Ambiguous Case)

Describe both possible triangles in the space below

14Construct a triangle with sides 4.9cm, 4.8cm and holding angles 51° and 38°.

Describe your construction steps in the space below

15Construct a triangle using sides 7cm, 6cm, 5cm. Verify that the medians are concurrent.

Describe construction and verification steps

Q3. Write detailed answers of the following questions. (Answer any 2) (2 × 5 = 10 marks)

1. Perpendicular Bisector and Medians Construction

Draw perpendicular bisector of the triangle EFG with \( mEF = 5cm, mFG = 2.5cm, mEG = 4.3cm \). Find the medians. (Example 7)

2. Angle Bisector Construction

Draw angle bisector of a triangle FGH if: (Example 8) \( mFG = 5.2cm, mGH = 4.1cm \) and \( m\angle FGH = 120^\circ \).

3. Ambiguous Case Analysis

Construct the following triangles and find whether there exists any ambiguous case.

(i) \( \triangle BCD \); \( mBC = 5cm \), \( m\angle B = 60^\circ \), \( mCD = 4.7cm \)

(ii) \( \triangle KLM \); \( mLM = 6cm \), \( m\angle M = 42^\circ \), \( mLN = 5cm \)

Q1. Choose the correct option. (10 × 1 = 10 marks)

Q2. Write down short answers of following questions. (15 × 2 = 30 marks)

1Define the term “Loci”. Write its importance.

2Define Isosceles Triangle. Also give example.

3State Triangle Inequality Theorem. Also give example.

4When does the Ambiguous Case (SSA) occur? Give example.

5Define Perpendicular Bisector of a triangle. Also give example.

6Define Median of a triangle. Also give example.

7What is Point of Concurrency?

8Define Altitudes of a triangle. Also give example.

9Define Orthocenter of a triangle. Also give example.

10Construct a triangle of sides 5.3cm, 5.9cm and 6.2cm. (Example 1)

Describe your construction steps in the space below

11Construct a triangle BCD in which measures of two sides are 5.5cm and 4.2cm and measure of their included angle is 60°. (Example 2)

Describe your construction steps in the space below

12Draw a triangle CDE when \( mDE = 4.3cm \), \( m\angle D = 30^\circ \) and \( m\angle E = 120^\circ \). (Example 3)

Describe your construction steps in the space below

13Construct triangles DEF and D’E’F’ when \( mDE = 6cm \), \( m\angle D = 30^\circ \) and \( mEF = 3.6cm \) (Example 5 – Ambiguous Case)

Describe both possible triangles in the space below

14Construct a triangle with sides 4.9cm, 4.8cm and holding angles 51° and 38°.

Describe your construction steps in the space below

15Construct a triangle using sides 7cm, 6cm, 5cm. Verify that the medians are concurrent.

Describe construction and verification steps

Q3. Write detailed answers of the following questions. (Answer any 2) (2 × 5 = 10 marks)

1. Perpendicular Bisector and Medians Construction

Draw perpendicular bisector of the triangle EFG with \( mEF = 5cm, mFG = 2.5cm, mEG = 4.3cm \). Find the medians. (Example 7)

2. Angle Bisector Construction

Draw angle bisector of a triangle FGH if: (Example 8) \( mFG = 5.2cm, mGH = 4.1cm \) and \( m\angle FGH = 120^\circ \).

3. Ambiguous Case Analysis

Construct the following triangles and find whether there exists any ambiguous case.

(i) \( \triangle BCD \); \( mBC = 5cm \), \( m\angle B = 60^\circ \), \( mCD = 4.7cm \)

(ii) \( \triangle KLM \); \( mLM = 6cm \), \( m\angle M = 42^\circ \), \( mLN = 5cm \)

Mathematics Examination

MATHEMATICS EXAMINATION PAPER

Q1. Choose the correct option. (10 × 1 = 10 marks)

Q2. Write down short answers of following questions. (15 × 2 = 30 marks)

Q3. Write detailed answers of the following questions. (Answer any 2) (2 × 5 = 10 marks)

1. Perpendicular Bisector and Medians Construction

2. Angle Bisector Construction

3. Ambiguous Case Analysis

Mathematics Examination

MATHEMATICS EXAMINATION PAPER

Q1. Choose the correct option. (10 × 1 = 10 marks)

Q2. Write down short answers of following questions. (15 × 2 = 30 marks)

Q3. Write detailed answers of the following questions. (Answer any 2) (2 × 5 = 10 marks)

1. Perpendicular Bisector and Medians Construction

2. Angle Bisector Construction

3. Ambiguous Case Analysis