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Level 9 0 /9 skills Course: Geometry (FL B.E.S.T.)

Unit 5 Quiz 2 Math>Geometry (FL B.E.S.T.)>Relationships in triangles and quadrilaterals>Quiz 2 © 2024 Khan Academy Terms of usePrivacy PolicyCookie Notice

Quiz 2 Google Classroom Microsoft Teams Share to Microsoft Teams Problem Given:

[\overleftrightarrow{BD}] is the perpendicular bisector of segment

[\overline{AC}].

[\overline{BD}] is [3] units long.

[\overline{AC}] is [8] units long. Naomi was asked to show that point [D] is equidistant from points [A] and [C]. Line segment A C with line B D being a perpendicular bisector at point B. [C] [D] [A] [B] Fill in the blanks in Naomi's solution. Since

[\overleftrightarrow{BD}] bisects

[\overline{AC}], we know that both

[\overline{AB}] and

[\overline{BC}] are units long. We are given that

[\overline{BD}] is [3] units long.

[\overleftrightarrow{BD}] is perpendicular to

[\overline{AC}], so [\triangle ABD] is a right triangle. Applying the Pythagorean theorem to [\triangle ABD] shows that the length of the hypotenuse is units. We can follow a similar process on [\triangle CBD] to show that

have the same length, so point [D] must be equidistant from points [A] and [C].

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