GANITA PRAKASH · GRADE 7 · PART II · CHAPTER 1
ANGLE — Two angles and a side
Think first. Use AI purposefully. Verify always.
DISCOVER
Start with a sketch and a prediction.
Two angles are 35° and 75°. What is the third angle, and how does knowing it help fix a triangle?
Try on paper first. Use the model to test your idea before accepting the explanation.
Understand
ASA fixes two angles and their included side. AAS also guarantees congruence: the third angle is determined by the 180° sum, converting the data into an ASA determination.
Key Ideas
AAS is valid even though the side is not between the two originally stated angles.
Visualise
Recover the missing angle
BC = 4 cm. Predict the missing angle before revealing it.
Method
Identify the side and both endpoint angles. If one endpoint angle is missing, compute it from the angle sum. Construct the two rays at the side endpoints and use their intersection.
Worked Example
Given
∠A = ∠X = 35°, ∠C = ∠Z = 75°, BC = YZ = 4 cm.
To Prove
△ABC ≅ △XYZ
Property
Angle sum followed by ASA, equivalently AAS.
Proof
- ∠B = ∠Y = 180° − 35° − 75° = 70°.
- The endpoint angles B, C match Y, Z and the included sides BC, YZ are equal.
Result
△ABC ≅ △XYZ.
AIMS Method
- A — Attempt independently
Sketch and predict before using a criterion. - I — Investigate the idea
Separate given facts from visual assumptions. - M — Make connections
Match vertices, sides and angles consistently. - S — Scrutinise your reasoning
Check each hypothesis and justify the conclusion.
Think first. Use AI purposefully. Verify always.
Focused Practice
In the source ASA example, ∠B = 50°, ∠C = 30° and BC = 5 cm. Find ∠A.
Check & Feedback
Name the exact given facts, state a valid criterion or explain why none applies, and check the vertex order.
Textbook connection: Ganita Prakash · Grade 7 · Part II · Chapter 1 — Geometric Twins · printed page 15