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
- Use similarity to relate an altitude to hypotenuse segments.
- 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
An altitude from a right angle meets the hypotenuse and splits it into lengths 4 cm and 9 cm. Find the altitude.
Why this math matters
Recognize a hidden similarity relationship inside a subdivided right triangle. 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.
Split a right triangle into similar triangles
PausedQuestion: Start with the question. Paused.
Question
Start with the question
An altitude from a right angle meets the hypotenuse and splits it into lengths 4 cm and 9 cm. Find the altitude.
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
The two smaller triangles are similar
Their acute angles correspond because each has one right angle and shares an angle relation with the original.
Develop the calculation
h/4=9/h, so h²=36
The altitude is a geometric mean of the two hypotenuse segments.
Check and interpret
h=6 cm
The positive root gives the perpendicular distance.
The result
h=6 cm
The positive root gives the perpendicular distance.
Common mistakes to catch
- The altitude must start at the right-angle vertex and end on the hypotenuse.
- Do not use the arithmetic average instead of the geometric mean.
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 two hypotenuse segments are 2 and 8, find the altitude.
Show a hint
Use h²=2×8.
Reveal answer and explanation
4
√16=4.
Practice 2
In the main example, what is the full hypotenuse length?
Show a hint
Add its two adjacent pieces.
Reveal answer and explanation
13 cm
4+9=13; the altitude is not itself a hypotenuse piece.
Take the idea with you
Recognize a hidden similarity relationship inside a subdivided right triangle.
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: Choose sine, cosine, or tangent from the known sides
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