Geometry Class 10 Quiz

Instructions & Information

• All questions are compulsory
• Calculators are not allowed
• Only the first attempt for multiple choice questions (MCQs) is graded
• The correct answer alternative (A, B, C, or D) for MCQs, along with the sub-question number, is required
• Draw figures when needed
• Construction marks must be clear and not erased
• Diagrams are essential for proving theorems

Multiple Choice Questions (MCQ)

• Δ ABC ~ Δ PQR ; if AB = 4 cm, PQ = 6 cm, and QR = 9 cm, then BC = 6 cm
• ∠PRQ is inscribed in arc PRQ of a circle with center O. If ∠PRQ = 75°, then arc PRQ = 150°
• Seg AB is parallel to the Y-axis and the coordinates of point A are (1, 3). The coordinates of point B can be (1, -3)
• The Pythagorean triplet that is NOT a Pythagorean triplet is (12, 9, 15)

Sub-Questions (B)

• In a figure, given AB ⊥ BC and DC ⊥ BC. If AB = 3 and DC = 4, find the ratio of areas A(ΔABC) / A(ΔDCB)
• Given the diagonal of a square is 12√2 cm, find the side length
• Given tan θ = √3, find the value of θ
• Given a circle with center C and radius 6 cm. Line AB is a tangent at point A. Find the measure of ∠CAB.

(Note: Further sub-questions are given for different problems)

Complete the Following Activity (A)

• In Δ ABC, line PQ is parallel to BC. If AP = 10, PB = 12, and AQ = 15,then find QC. The activity shows calculations to find QC. The result is QC = 18cm.

Find ∠AOB and ∠ACB

• In a circle with center O, chord AB is equal to the radius of the circle. ∠AOB = ? (Answer: 60°) and ∠ACB = ? (Answer: 30°)

Distance between Points

• Find the distance between points P(6, -6) and Q(3, -7). The solution method utilizes the distance formula. The answer is √13.

Additional Sub-Questions

• Find EF in Δ DEF, where ∠E = 90°, DE = 33 cm, and DF = 65 cm.
• Two arcs formed by a chord of a circle have measures 2x and 7x degrees. Find the measure of the minor arc.
• Find the coordinates of the centroid for triangle ABC given vertices: A(-7, 6), B(2, 2), and C(8, 5).
• If sin θ = 7/25, find the value of cos θ

Prove That...

• In a right-angled triangle, the perpendicular segment to the hypotenuse from the opposite vertex is the geometric mean of the segments into which the hypotenuse is divided.
• Cyclic quadrilateral ABCD; AB = AD, and ∠BCD = 70°. Find: m(arc BCD), m(arc BAD), and ∠ABD.

Additional Geometry Problems

(Geometry problems are listed, including specific figures and constructions)

Circle with Centre P

• Draw a circle with center P and radius 3.5 cm.
• Draw an arc AB of 120° measure.
• Draw tangents to the circle at points A and B.

Prove that...

• 1 - cos A / √1 + cos A = cosec A - cot A.

• Given consecutive angles of a cyclic quadrilateral are congruent, prove that one pair of opposite sides is parallel and the other pair is congruent.

• Δ LMN ~ Δ LQP. Provide given values and construct the triangles.

• In Δ PQR, seg XY || side QR, M and N are midpoints of PY and PR. Prove seg XM || seg QN and ΔPXM ≅ ΔPQN.

Angle Bisector and Circle

• Draw angle ABC of 65°.
• Draw ray BM which bisects angle B.
• Take point P on BM such that BP = 4 cm.
• Draw perpendicular from P to BC.
• Draw a circle with center P and radius equal to the perpendicular length.
• Determine the relation of the circle to the angle's arms.
• Given A(2, 1) and B(-3, 6) & ratio 2:3, determine if point P lies on the line x - 5y + 15 = 0.

Test your knowledge of geometry concepts with this comprehensive quiz. Covering similarity of triangles, angles inscribed in circles, coordinate geometry, and Pythagorean triplets, this quiz is designed for 10th-grade students. Make sure to draw diagrams where necessary and only utilize your first attempt for grading!