Speedy Delivery

ID: tuliv-garil
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Speedy Delivery

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Problem 1

1) Which construction can be used to determine whether point CC is closer to point AA or point BB?

a) Construct triangle ABC\text{Construct triangle } ABC \text{. }b) Construct a line perpendicular to segment AB through point C\text{Construct a line perpendicular to segment } AB \text{ through point } C \text{. }c) Construct the bisector of angle ACB\text{Construct the bisector of angle } ACB \text{. }d) Construct the perpendicular bisector of segment AB.\text{Construct the perpendicular bisector of segment } AB \text{.}
Problem 2

2) The diagram is a straightedge and compass construction. Lines ll, mm, and nn are the perpendicular bisectors of the sides of triangle ABCABC. Select all the true statements. Write each corresponding letter in the answer box and separate letters with commas.

a) Point EE is closer to point AA than it is to point CC. \quad\quad b) Point LL is closer to point BB than it is to point AA.

c) Point DD is closer to point BB than it is to point CC. \quad\quad d) Point JJ is closer to point AA than it is to point BB or point CC.

e) Point KK is closer to point CC than it is to point AA or point BB. \quad\quad f) Point LL is closer to point CC than it is to point AA or point BB.

Problem 3

3) Decompose the figure into regions that are closest to each vertex.

A template for answering this question. Ask your instructor for an alternative.

4) Explain or show your reasoning.

Problem 4

5) Which construction could be used to construct an isosceles triangle ABCABC given line segment ABAB?

a) Mark a third point C not on segment AB. Draw segments AC and BC\text{Mark a third point } C \text{ not on segment } AB \text{. Draw segments } AC \text{ and } BC \text{. }b) Label a point C on segment AB and construct a line perpendicular to AB through point C Draw segments AC and BC\text{Label a point } C \text{ on segment } AB \text{ and construct a line perpendicular to } AB \text{ through point } C \text{. } \newline \text{ Draw segments } AC \text{ and } BC \text{. }c) Construct the perpendicular bisector of segment AB. Mark the intersection of this line and AB and label it C Draw segments AC and BC.\text{Construct the perpendicular bisector of segment } AB \text{. Mark the intersection of this line and } AB \text{ and label it } C \text{. } \newline \text{ Draw segments } AC \text{ and } BC \text{.}d) Construct the perpendicular bisector of segment AB Mark any point C on the perpendicular bisector except where it intersects AB. Draw segments AC and BC.\text{Construct the perpendicular bisector of segment } AB \text{. } \newline \text{ Mark any point } C \text{ on the perpendicular bisector except where it intersects } AB \text{. Draw segments } AC \text{ and } BC \text{.}
Problem 5

6) Select all true statements about regular polygons. Write each corresponding letter in the answer box and separate letters with commas.

a) All angles are right angles. \quad\quad b) All angles are congruent. \quad\quad c) All side lengths are equal.

d) There are exactly 4 sides. \quad\quad e) There are at least 3 sides.

Problem 6

7) This diagram shows the beginning of a straightedge and compass construction of a rectangle.

The construction followed these steps:

1. Start with two marked points AA and BB

2. Use a straightedge to construct line ABAB

3. Use a previous construction to construct a line perpendicular to ABAB passing through AA

4. Use a previous construction to construct a line perpendicular to ABAB passing through BB

5. Mark a point CC on the line perpendicular to ABAB passing through AA

Explain the steps needed to complete this construction.

A template for answering this question. Ask your instructor for an alternative.
Problem 7

This diagram is a straightedge and compass construction.

A template for answering this question. Ask your instructor for an alternative.

8) Is it important that the circle with center BB passes through DD and that the circle with center DD passes through BB?

True or false? Write below.

9) Show or explain your reasoning.