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 AA similarity and match corresponding 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
Triangles ABC and DEF have A=D=40° and B=E=65°. If AB=6 and DE=9, what is the scale from ABC to DEF?
Why this math matters
Use a smaller measurable triangle to infer lengths in a similar larger shape. 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 angle agreement to scale triangles
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Triangles ABC and DEF have A=D=40° and B=E=65°. If AB=6 and DE=9, what is the scale from ABC to DEF?
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
C=F=180°−40°−65°=75°
Two equal angle pairs force the third pair equal.
Develop the calculation
DE/AB=9/6=3/2
Use corresponding sides determined by the vertex order.
Check and interpret
Scale factor = 1.5
If AC=8, then corresponding DF=12 under this same scaling.
The result
Scale factor = 1.5
If AC=8, then corresponding DF=12 under this same scaling.
Common mistakes to catch
- Pair sides opposite corresponding angles.
- Similarity preserves angles but not necessarily lengths.
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 BC=10, what is EF?
Show a hint
Apply the same scale to corresponding sides.
Reveal answer and explanation
15
10×1.5=15.
Practice 2
Do equal angles alone make the triangles congruent?
Show a hint
Similarity allows a nonunit scale.
Reveal answer and explanation
No
The main triangles differ in size because corresponding sides are in ratio 3:2.
Take the idea with you
Use a smaller measurable triangle to infer lengths in a similar larger shape.
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: Dilate from a center other than the origin
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