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Grade 10 · Right triangles

Architect's sketch: Verify a coordinate-distance model

Architect's sketch investigation: verify a coordinate-distance model. Change the quantities, follow the motion, and explain the result using the displayed mathematical relationship.

Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.

Watch the relationship

Paused
Architect's sketch: Verify a coordinate-distance model. First square area: 81. Second square area: 100. Combined area revealed: 0. Hypotenuse: 13.454Square the legs, add, then take a root910Square areas81100a² + b² = 181; c = 13.454
The theorem is applied only to a Euclidean right triangle with positive leg lengths. The triangle has equal axis scale, while the area bars use a separate common scale and are not drawn on its sides.

Starts paused. Play once, pause anywhere, or use Step to inspect the mathematics. Playback stops when this panel leaves the screen.

Make it your experiment

Change one value. Notice what follows.

The controls adjust the model. Numbers below describe the current frame. Decimals are rounded.

First square area
81
Second square area
100
Combined area revealed
0
Hypotenuse
13.454

HD animation studio

From experiment to screen.

Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.

Understand what you are seeing

The idea behind the motion.

For a right triangle, the square of the longest side equals the sum of the squares of the two legs. Square areas provide the comparison; the hypotenuse itself is the positive square root of their sum. Adding side lengths is not a substitute for this theorem. This investigation begins with first leg a = 9; second leg b = 10. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.

A relationship to keep

c² = a²+b²; c = √(a²+b²)

Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.

  1. STEP 1

    Represent the given quantities

    Locate the marked right angle and identify the two legs meeting there.

  2. STEP 2

    Follow the changing model

    Playback reveals the two square-area contributions beside the triangle and their combined total.

  3. STEP 3

    Check and explain the relationship

    Take the positive square root to recover a length, then square the answer to check the original identity.

Your turn to explain

Make a prediction. Test your reasoning.

Architect's sketch: A right triangle has legs 9 and 10. Find the hypotenuse.

Use the values specified in the question. Reset restores the initial values for this investigation.

Compare your explanation

√(181) ≈ 13.454 length units. The positive root represents a length.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 10 · Geometry

Derive distance from horizontal and vertical changes

Use the Pythagorean theorem for the distance between two planar points.