# Geometry in London

### Liam Goble-Garratt

*All answers are below the questions.

## Problem #1

## Is the West Centered?

This church, in London, England, has a clock on it. Is the clock in the center of the left tower of the cathedral? Which construction would you use to determine this?

## Problem #2

## Double Decker Dilemma

Given the information that the two horizontal lines are parallel, what is the measure of x? Also, name the relationship between the two lower angles.

## Problem #3

## Arsenal Arithmetic

Using this large A outside Emirates Stadium in London, England, find the value of x. Bonus! Now that you have these two angles what is the measure of the third angle?

## Problem #4

## Union Jack Drawback

Given the measures for the other angles, what is the value of x?

## Problem #5

## It seems we are in a pickle...

This building in London is known as the Gherkin. With what postulate can you prove these two triangles similar? What is the value of x? (Not drawn to scale)

## Problem #6

## London Bridge is Going Up...

Here are two triangles formed from London Bridge. What postulate proves triangle ABC congruent to triangle DCB?

## Problem #7

## Are You Sharp Enough for This?

One side of this building in London, the Shard, is a triangle. If two sides of the triangle measure 320 and 110, what can the measure of the third side be if it is between those two values?

## Problem #8

## Palace Predicament

If there are palace guards at the Royal Palace in London then the queen is safe.

If there are palace guards at the Royal Palace in London = G

Then the queen is safe = B

According to this statement, ~G --> ~B, how is the queen?

## Problem #9

## Great Britain Grid

James is at 1,4 and Sally is at 5, 1 and they both are meeting at the edge of the Thames at 6,4. Since the can take a boat over the river, using the 2 dimensional distance formula, who has further to travel to the meeting place on the river?

## Problem #10

## Do You Have an Eye for Geometry?

Using the spokes on the London Eye, what is the value of x?

## Answers!

#1. The answer to this problem is yes, the clock is centered. You would use the midpoint of a line segment construction as seen below.

#2. The solution to this dilemma is 107 degrees. Also, the relationship between these two is that they are mutual friends. Just kidding, they are consecutive interior angles (and supplementary).

#3. We know that this triangle is isosceles because two sides have the same length. We also know that if two side of a triangle are congruent, the angles opposite those two sides are also congruent. Therefore, the answer is 48 degrees. The bonus answer is 84 degrees.

#4. The value of x is 47 degrees.

#5. The triangles are similar by SSS. The value of x is 7.

#6. The congruence postulate needed is SAS. We use the given side and angle, then the reflexive property for segment BC=CB.

#7. 430>x>210. By the way, these are not the actual dimensions of the Shard.

#8. The statement reads, "If there are no palace guards at the Royal Palace in London then the queen is not safe." The queen is in danger, call in MI6!