Question

quiz 14 date score plane geometry sections 2.14–2.16 completion: write the word(s) in the blank at the left that best completes the statement. 1. the sum of the four angles of a quadrilateral is equal to ?. 2. the perpendicular to the base of an isosceles triangle that passes through the vertex will also ? the vertex angle. 3. the shortest line that can be drawn from a point to a line is the ?. proof: fill in the steps to complete the proof. 4. given: ab > bd, ∠adb = ∠c prove: ad > dc (with a triangle diagram labeled a, b, c, d) proof: statements reasons © 2006–2015 educational ventures, inc. all rights reserved. any unauthorized copying, aberation, distribution, transmission, display, or other use of this material is prohibited.

Explanation:

Question 1

Step1: Recall quadrilateral angle sum

A quadrilateral can be divided into two triangles. Each triangle has an angle sum of \(180^\circ\), so two triangles give \(2\times180^\circ = 360^\circ\).

Step2: Confirm the sum

The sum of the interior angles of any quadrilateral is \(360^\circ\) (or 360 degrees).

Step1: Recall isosceles triangle properties

In an isosceles triangle, the perpendicular from the vertex to the base (altitude) has the property of bisecting the vertex angle (and also bisecting the base).

Step2: Determine the action

The perpendicular to the base through the vertex will bisect the vertex angle.

Step1: Recall distance from point to line

The shortest distance from a point to a line is the length of the perpendicular segment from the point to the line.

Step2: Identify the segment

This segment is called the perpendicular (or perpendicular segment, or altitude in some contexts, but the key term here is "perpendicular" as the shortest line is the perpendicular line segment).

Answer:

\(360^\circ\) (or 360 degrees)

Question 2