Geometry

Question 1

What can you assume about whether or not drawings are “to scale” in Geometry problems?

Answer 1

1. Never assume drawings are to scale in DS
2. In PS, you can infer more often (right angles, etc.) since there has to be 1 answer. But still be careful.

Question 2

What is true about regular polygons in Geometry?

Answer 2

For all regular polygons (circles, squares, equilaterial triangles), if you know one non-angle dimension (like a side length) of the shape, you can find all others. Regular polygons = “equilateral” polygons

Question 3

If you have multiple shapes in a Geometry problem, what should come to mind?

Answer 3

Think about how these shapes “interact.” Do they share a side? Can you use one to determine the area of the other?

Question 4

Q2 Free Prep Hour - try it without looking at answer.

Answer 4

Answer = B.

1. Statement 1: NS. Could be equilateral, could be isosceles, we just don’t know dimensions of the triangle. And JUST with the circle info, we can’t infer sides of triangle.
2. Statement 2: With the area of the circle, you can find the radius (regular polygon rule).
   
   • You also know the angles of the triangle (60-60-60) b/c S2 tells you.
   • SO you can find a side by creating a 30-60-90 triangle. Thus you can find all sides / the perimeter.
3. C Trap: CLEARLY combined they’ll be sufficient (if you have 1 side and you know it’s equilateral, you can solve).

Question 5

What are the side ratios of a 30-60-90 triangle?

Answer 5

Write it out on a piece of paper!

• TIP: ​If you have an equilateral triangle, you also have a 30-60-90 triangle inscribed! (See Q2 Prep Hour)

Question 6

What are the side ratios of a 45-45-90 triangle?

Answer 6

Write it out on a piece of paper!

Question 7

Q3 Free Prep Hour - try it without looking at answer.

Answer 7

Answer = C.

1. Draw the triangle on the coordinate plane.
2. Draw the rectangle around the triangle. Find the area of that rectangle (in this case 70).
3. Then start “hacking away” at the areas around the original triangle. Find the areas of the smaller triangles and start subtracting them from rectangle.

Question 8

Q4 Free Prep Hour - try it without looking at answer.

Answer 8

Answer = D

• You have an incribed angle across from a line that passes through the center of the circle: that inscribed angle must be 90 degrees (inscribed/central angle rule)!
• SO, since you’re given 30 degrees and you know that one other angle is 90 degrees, it must be a 30-60-90 triangle.
• You are given the circumference SO you can find out diameter, and find all sides of the triangle,

Can also ESTIMATE here.

• 6(π)(root 3) OR (6)(3)(1.7) is about 33.
• SO that means that 1/2 the circumference is about 16
• And half that is about 8
• So BC = a little more than 8, which means 9 is the closest.

Question 9

If you have a central angle in a circle (one that pases thru the center of the circle) what is true about other angles that open up the same arch?

Answer 9

The central angle is ALWAYS DOUBLE an inscribed angle that opens up the same arch.

• This is helpful b/c if a line passes thru the center of a circle (diameter), an incribed angle on either side will be 90 degrees.

Question 10

Q1 Free Prep Hour - try it without looking at answer.

Answer 10

Answer is B.

• Straight up process of elimination by “solving” answer choices and finding their values.
• Answer MUST HAVE π in it! You are subtracting Circle Stuff from Rectangle Stuff, so there will be a π in there somewhere.