Worksheet Thales' Intercept Theorem

Applet Reference

Thales' Intercept Theorem Applet borrowed from patelk https://www.geogebra.org/m/uSQf4GWH

About Thales' Intercept Theorem

Which of the following statements is true about Thales' Intercept Theorem?

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A
A) If a line intersects two sides of a triangle and is parallel to one side, the two triangles formed are congruent.
B
B) If a line intersects two sides of a triangle and is parallel to one side, the two triangles formed are similar, and their corresponding sides are proportional.
C
C) The line must be perpendicular to one side of the triangle for Thales' Intercept Theorem to apply.
D
D) Thales' Intercept Theorem applies only to isosceles triangles.

In the construction of Thales' Intercept Theorem, which of the following is required for the smaller triangle to be similar to the original triangle?

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A
A) The line must be parallel to one of the sides of the triangle.
B
B) The line must be perpendicular to one of the sides of the triangle.
C
C) The line must be drawn at an angle of 45 degrees.
D
D) The triangle must be isosceles.

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Thales' Intercept Theorem Construction

In a triangle △ABC, if a line is drawn parallel to side BC and intersects sides AB and AC at points D and E, which of the following is true?

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A
A) △ADE∼△ABC and AD/AB=AE/AC.
B
B) △ADE∼△ABC and AD/AB=AE/BC.
C
C) △ADE∼△ABC and AD/AC=AE/AB.
D
D) The two triangles are not similar.

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Relationship between the corresponding sides

If in a triangle △ABC, a line parallel to side BC divides sides AB and AC at points D and E, what is the relationship between the corresponding sides of the smaller and original triangles?

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A
A) The corresponding sides are congruent.
B
B) The corresponding sides are proportional.
C
C) The corresponding sides are equal.
D
D) The corresponding sides are perpendicular.

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Worksheet Thales' Intercept Theorem

Applet Reference

About Thales' Intercept Theorem

Thales' Intercept Theorem Construction

Relationship between the corresponding sides

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