Class 7 Geometry Worksheet - Triangles, Congruence & Parallel Lines PDF

Advanced geometry worksheet for Class 7 with 24 problems covering triangle angle properties, SSS/SAS/ASA/RHS congruence criteria, parallel line theorems, Pythagoras theorem applications, and geometric proofs. Complete solutions with detailed working included.

Essential Formulas & Properties

Triangle Properties:

Sum of angles = 180°

Exterior angle = Sum of two opposite interior angles

Sum of any two sides > Third side

Congruence Criteria:

SSS: Side-Side-Side

SAS: Side-Angle-Side

ASA: Angle-Side-Angle

RHS: Right angle-Hypotenuse-Side

Parallel Lines:

Corresponding angles are equal

Alternate interior angles are equal

Co-interior angles sum to 180°

Solved Example - Congruence Problem

Problem: In triangles ABC and PQR, AB = PQ = 7 cm, ∠B = ∠Q = 70°, and BC = QR = 8 cm. Prove that the triangles are congruent.

Solution:

Given:

AB = PQ = 7 cm

∠B = ∠Q = 70°

BC = QR = 8 cm

In △ABC and △PQR:

AB = PQ (given)

∠B = ∠Q (given)

BC = QR (given)

Therefore, △ABC ≅ △PQR by SAS (Side-Angle-Side) criterion.

Sample Practice Problems

In a triangle ABC, ∠A = 65° and ∠B = 45°. Find ∠C

The angles of a triangle are in the ratio 2:3:4. Find all three angles

The sides of a triangle are 7 cm, 24 cm, and 25 cm. Check if this forms a right-angled triangle using Pythagoras theorem

In triangles ABC and DEF, AB = DE = 5 cm, BC = EF = 6 cm, and AC = DF = 7 cm. Are the triangles congruent? If yes, by which criterion?

Two right triangles have equal hypotenuses and one equal side. Are they congruent? Name the criterion

Two parallel lines are cut by a transversal. If the co-interior angles are (3x + 20)° and (2x + 10)°, find the value of x and both angles

A ladder 25 m long reaches a window 24 m above the ground. How far is the foot of the ladder from the base of the wall?

In triangle PQR, PQ = PR = 10 cm and QR = 12 cm. Find the altitude from P to QR

Scoring Guide

40-48 marks: Excellent - Outstanding understanding of geometry concepts!

32-39 marks: Very Good - Keep up the great work!

24-31 marks: Good - You're doing well! Practice more complex problems

Below 24 marks: Need Practice - Review concepts and try again

Study Tips for Geometry Success

Master the Basics: Understand all angle properties and triangle properties thoroughly before moving to advanced topics

Practice Constructions: Regular practice with compass and ruler improves accuracy and understanding

Draw Diagrams: Always draw neat, labeled diagrams - they make problems much easier

Learn Congruence Criteria: Memorize SSS, SAS, ASA, and RHS - know when to use each one

Understand Proofs: Don't just memorize steps - understand the logical flow of geometric proofs

Problem-Solving Tips

For parallel lines: Look for corresponding, alternate, or co-interior angles

For triangles: Start by finding the sum of angles = 180°

For isosceles triangles: Remember base angles are equal

For word problems: Draw and label the diagram first

Use Pythagoras theorem when you see right angles

Common Pitfalls

Don't confuse corresponding angles with alternate angles

Remember that exterior angle equals sum of opposite interior angles, not all angles

In congruence, order of vertices matters

Check triangle inequality before assuming three sides can form a triangle

Always show proper reasoning in proof questions

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