Geometry in London
*All answers are below the questions.
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?
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.
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?
Union Jack Drawback
Given the measures for the other angles, what is the value of x?
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)
London Bridge is Going Up...
Here are two triangles formed from London Bridge. What postulate proves triangle ABC congruent to triangle DCB?
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?
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?
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?
Do You Have an Eye for Geometry?
Using the spokes on the London Eye, what is the value of x?
#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!