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Thales' theorem and proportions

Mathematics — first biennium · Lesson

Biennium · Common core

Thales' theorem and proportions

Parallel lines cut two transversals into proportional segments. The proportion expresses the same scale on both sides.

Key idea
Formula matematica
Similar example
Formula matematica

Prerequisites: Parallel lines and proportions

Goal: Use parallelism to establish proportions between corresponding segments.

What you need to know before the exercises

In this lesson: Use parallelism to establish proportions between corresponding segments.

How to proceed: Match corresponding segments in the same order. The scale factor must be the same on both transversals.

You can already assume: Parallel lines and proportions.

Try it now

Complete a proportion generated by corresponding segments.

Guided

Completed exercises: 0/5 · Correct on first attempt: 0

How to reason

Match corresponding segments in the same order. The scale factor must be the same on both transversals.

Data / situation: AB=4, A'B'=12, AC=4; the corresponding lines are parallel. Find A'C'.

Your competency map

What you need to know for Thales' theorem and proportions

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Current topic Strong skill Review due Needs reinforcement To be mastered Optional support

Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.

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