Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 10 chapters and video availability01 · Read and understand
What you will learn
- Apply side-angle-side when the angle lies between the known sides.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Algebraic equations, ratios, angle and area facts, and basic coordinate geometry.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Two triangles have corresponding side lengths 5 cm and 8 cm with included angle 60° in each. Are they congruent?
Why this math matters
Use sufficient measurements to establish that two manufactured triangular shapes match exactly in the model. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use Euclidean geometry and the angle, parallelism, similarity, or congruence conditions stated; a sketch alone does not establish them.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Use an included angle in a congruence argument
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Two triangles have corresponding side lengths 5 cm and 8 cm with included angle 60° in each. Are they congruent?
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the conditions
Match the 5 cm sides and the 8 cm sides
Corresponding parts must be paired consistently.
Develop the calculation
The 60° angle lies between those two sides
The included-angle condition fixes their relative placement.
Check and interpret
The triangles are congruent by SAS
Rigid motion, possibly with reflection, aligns one complete triangle with the other.
The result
The triangles are congruent by SAS
Rigid motion, possibly with reflection, aligns one complete triangle with the other.
Common mistakes to catch
- The angle in SAS must be included between the known sides.
- Write correspondence in a consistent vertex order.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
If the 60° angle is not between the two known sides, does SAS apply?
Show a hint
Check the exact location of the angle.
Reveal answer and explanation
No
The data form an SSA pattern instead, which can be ambiguous.
Practice 2
Can congruent triangles have different orientations on the page?
Show a hint
Congruence permits rigid motions.
Reveal answer and explanation
Yes
Translation, rotation, or reflection changes placement but preserves all lengths and angles.
Take the idea with you
Use sufficient measurements to establish that two manufactured triangular shapes match exactly in the model.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: See why side-side-angle can give two triangles
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