Speedy Delivery

ID: tuliv-garil
Illustrative Math
Subject: Geometry

Speedy Delivery

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Problem 1

1) Which construction can be used to determine whether point ﻿$C$﻿ is closer to point ﻿$A$﻿ or point ﻿$B$﻿?

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

2) The diagram is a straightedge and compass construction. Lines ﻿$l$﻿, ﻿$m$﻿, and ﻿$n$﻿ are the perpendicular bisectors of the sides of triangle ﻿$ABC$﻿. Select all the true statements. Write each corresponding letter in the answer box and separate letters with commas.

a) Point ﻿$E$﻿ is closer to point ﻿$A$﻿ than it is to point ﻿$C$﻿. ﻿$\quad\quad$﻿ b) Point ﻿$L$﻿ is closer to point ﻿$B$﻿ than it is to point ﻿$A$﻿.

c) Point ﻿$D$﻿ is closer to point ﻿$B$﻿ than it is to point ﻿$C$﻿. ﻿$\quad\quad$﻿ d) Point ﻿$J$﻿ is closer to point ﻿$A$﻿ than it is to point ﻿$B$﻿ or point ﻿$C$﻿.

e) Point ﻿$K$﻿ is closer to point ﻿$C$﻿ than it is to point ﻿$A$﻿ or point ﻿$B$﻿. ﻿$\quad\quad$﻿ f) Point ﻿$L$﻿ is closer to point ﻿$C$﻿ than it is to point ﻿$A$﻿ or point ﻿$B$﻿.

Problem 3

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

4) Explain or show your reasoning.

Problem 4

5) Which construction could be used to construct an isosceles triangle ﻿$ABC$﻿ given line segment ﻿$AB$﻿?

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

2. Use a straightedge to construct line ﻿$AB$﻿

3. Use a previous construction to construct a line perpendicular to ﻿$AB$﻿ passing through ﻿$A$﻿

4. Use a previous construction to construct a line perpendicular to ﻿$AB$﻿ passing through ﻿$B$﻿

5. Mark a point ﻿$C$﻿ on the line perpendicular to ﻿$AB$﻿ passing through ﻿$A$﻿

Explain the steps needed to complete this construction.

Problem 7

This diagram is a straightedge and compass construction.

8) Is it important that the circle with center ﻿$B$﻿ passes through ﻿$D$﻿ and that the circle with center ﻿$D$﻿ passes through ﻿$B$﻿?

True or false? Write below.

9) Show or explain your reasoning.