Geometric Twins Worksheet for Class 7 - Congruent Triangles PDF

Specialized congruence worksheet for Class 7 with 15 progressive problems focusing on identifying congruent triangles using SSS, SAS, ASA, and RHS criteria. Includes real-world applications, proofs, and complete solutions with detailed explanations.

What are Geometric Twins?

Just like human twins look identical, geometric twins are triangles that are exactly the same in shape and size - we call them CONGRUENT TRIANGLES!

In this worksheet, you'll become a detective who identifies which triangles are twins (congruent) and proves why they're twins using special criteria!

The 4 Ways to Prove Triangles are Twins

SSS (Side-Side-Side)

All three sides of one triangle equal the three sides of another triangle.

AB = DE, BC = EF, CA = FD

SAS (Side-Angle-Side)

Two sides and the angle between them in one triangle equal the corresponding parts in another.

AB = DE, ∠B = ∠E, BC = EF

ASA (Angle-Side-Angle)

Two angles and the side between them in one triangle equal the corresponding parts in another.

∠A = ∠D, AB = DE, ∠B = ∠E

RHS (Right-Hypotenuse-Side)

In right triangles, if the hypotenuse and one other side are equal, they're congruent!

∠B = ∠E = 90°, AC = DF, AB = DE

Worked Example: Finding Geometric Twins

Problem: In triangles ABC and XYZ, AB = 6 cm, BC = 8 cm, ∠B = 90°, XY = 6 cm, YZ = 8 cm, and ∠Y = 90°. Are they twins (congruent)?

Solution:

Step 1: Identify what we know

Both triangles are right-angled (∠B = ∠Y = 90°)

AB = XY = 6 cm

BC = YZ = 8 cm

Step 2: Find the hypotenuse using Pythagoras theorem

AC² = AB² + BC² = 6² + 8² = 36 + 64 = 100

AC = 10 cm

Similarly, XZ = 10 cm

Step 3: Apply congruence criterion

Since both are right triangles with equal hypotenuse and one equal side:

△ABC ≅ △XYZ by RHS criterion

Answer: Yes, they are geometric twins!

Sample Practice Problems

Triangle ABC: AB = 5 cm, BC = 6 cm, CA = 7 cm. Triangle PQR: PQ = 5 cm, QR = 6 cm, RP = 7 cm. Are they congruent?

Triangle ABC: ∠B = 90°, AC (hypotenuse) = 13 cm, AB = 5 cm. Triangle PQR: ∠Q = 90°, PR = 13 cm, PQ = 5 cm. Prove congruence using RHS

In triangle ABC, AB = AC (isosceles). D is the midpoint of BC. AD is the median. Prove that △ABD ≅ △ACD

Triangle ABC is equilateral with side 12 cm. Points D, E, F are midpoints of AB, BC, CA respectively. Prove that △AEF ≅ △BFD ≅ △CDE

ABCD is a square with side 10 cm. Diagonals AC and BD intersect at O. Prove that △AOB ≅ △BOC ≅ △COD ≅ △DOA

You have 6 sticks: two of 5 cm, two of 7 cm, and two of 9 cm. If you make two triangles using all 6 sticks, will they be congruent? Which criterion proves it?

Scoring Guide

26-30 marks: Master Detective - You've mastered congruence!

21-25 marks: Expert Detective - Excellent understanding!

16-20 marks: Good Detective - You're getting there!

11-15 marks: Junior Detective - Keep practicing!

Below 11 marks: Apprentice Detective - Review the concepts and try again!

Tips to Become a Master Twin Detective

Remember the 4 Criteria: Memorize SSS, SAS, ASA, and RHS - these are your detective tools!

Draw and Label: Always draw neat diagrams with proper labels - visual representation helps identify twins

Order Matters: When writing △ABC ≅ △DEF, corresponding vertices must be in matching order

Look for Right Angles: If you see 90°, think RHS for right triangles!

Check Given Information: Count what you know - 3 sides? SSS. 2 sides + included angle? SAS

Common Mistakes to Avoid

Don't use AAA (three angles) - it proves similarity, not congruence!

For SAS, the angle must be BETWEEN the two sides

For ASA, the side must be BETWEEN the two angles

RHS only works for RIGHT triangles

Corresponding vertices must match in congruence statements

Not checking if given angle is actually between the two given sides

Practice Proof Writing

Always state: "In △___ and △: ... Therefore, △ ≅ △___ by ___ criterion"

Show all corresponding equal parts clearly

State the congruence criterion at the end

Use proper mathematical notation and symbols

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