The Mid-Point Theorem (Grade 10 NSC Matric Mathematics): Quizzes

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The Mid-Point Theorem
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What two properties does the mid-point theorem guarantee about line DEDE joining mid-points?

DE∥BCDE \parallel BC and DE=12BCDE = \frac{1}{2}BC

If BC=24BC = 24 units and DD, EE are mid-points of ABAB and ACAC, what is the length of DEDE?

12 units

For which type(s) of triangles does the mid-point theorem work?

Any triangle type

What does the converse of the mid-point theorem state?

Line thru mid-point || to 2nd side bisects 3rd

Which geometric concepts are used to prove the mid-point theorem?

Congruent triangles and parallelograms

Which congruence method proves △ADE≅△CFE\triangle ADE \cong \triangle CFE in the mid-point theorem proof?

SAS (Side-Angle-Side)

In the proof, why is BCFDBCFD a parallelogram?

BD=CFBD = CF and BD∥CFBD \parallel CF

What ratio do similar triangles created by the mid-point theorem have?

1:2

Which is a practical application of the mid-point theorem?

Computer graphics for triangle subdivision

If DD and EE are mid-points of sides ABAB and ACAC in triangle ABCABC, then DEDE is parallel to?

BCBC

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