Quantatitve - Geometry

Question 1

How many degrees are in a straight line?

Answer 1

180°. If two angles form a straight line (linear pair), they must sum to 180°.

Question 2

How many degrees are in a full circle?

Answer 2

360°. Any angle formed by rotation around a point must total 360°.

Question 3

What is the sum of angles in a triangle?

Answer 3

180°. This is fixed for all triangles, regardless of shape.

Question 4

What is the sum of interior angles of a quadrilateral?

Answer 4

360°. Formula for polygons: (n − 2) × 180°.

Question 5

Formula for sum of interior angles of n-sided polygon?

Answer 5

(n − 2) × 180°. Example: Pentagon → (5−2)×180 = 540°.

Question 6

What are vertical angles?

Answer 6

Opposite angles formed by intersecting lines. They are always equal.

Question 7

What are complementary angles?

Answer 7

Two angles that sum to 90°.

Question 8

What are supplementary angles?

Answer 8

Two angles that sum to 180°.

Question 9

If two parallel lines are cut by a transversal, what are alternate interior angles?

Answer 9

They are equal. This is a common EA trap.

Question 10

Corresponding angles in parallel lines are?

Answer 10

Equal.

Question 11

What defines an isosceles triangle?

Answer 11

Two equal sides → two equal angles opposite those sides.

Question 12

What defines an equilateral triangle?

Answer 12

All sides equal → all angles 60°.

Question 13

What defines a right triangle?

Answer 13

One 90° angle.

Question 14

Pythagorean theorem?

Answer 14

a² + b² = c² (c is hypotenuse)

Question 15

Common Pythagorean triples?

Answer 15

3-4-5 5-12-13 8-15-17 Memorize these to avoid squaring.

Question 16

Area of triangle formula?

Answer 16

(1/2) × base × height.

Question 17

What is altitude of triangle?

Answer 17

Perpendicular height from base to opposite vertex.

Question 18

Triangle inequality rule?

Answer 18

Sum of any two sides must be greater than the third.

Question 19

If sides are 2, 3, and x, what must x satisfy?

Answer 19

1 < x < 5 Because 2+3 > x and |2−3| < x.

Question 20

If hypotenuse known and one leg known, how find other leg?

Answer 20

Use Pythagorean theorem.

Question 21

Circumference formula?

Answer 21

C = 2πr

Question 22

Area of circle formula?

Answer 22

A = πr²

Question 23

What is diameter in relation to radius?

Answer 23

d = 2r

Question 24

If diameter doubles, what happens to area?

Answer 24

Area quadruples (since r² effect).

Question 25

What is central angle?

Answer 25

Angle formed by two radii from center.

Question 26

Arc length formula?

Answer 26

(central angle / 360) × circumference.

Question 27

Sector area formula?

Answer 27

(central angle / 360) × total area.

Question 28

Area of rectangle?

Answer 28

Length × Width.

Question 29

Perimeter of rectangle?

Answer 29

2L + 2W.

Question 30

Area of square?

Answer 30

Side².

Question 31

Diagonal of square formula?

Answer 31

Side × √2.

Question 32

Area of parallelogram?

Answer 32

Base × Height.

Question 33

Area of trapezoid?

Answer 33

(1/2)(base₁ + base₂) × height.

Question 34

Slope formula?

Answer 34

(y₂ − y₁)/(x₂ − x₁)

Question 35

Distance formula?

Answer 35

√[(x₂ − x₁)² + (y₂ − y₁)²]

Question 36

Midpoint formula?

Answer 36

((x₁ + x₂)/2 , (y₁ + y₂)/2)

Question 37

Horizontal line slope?

Answer 37

0.

Question 38

Vertical line slope?

Answer 38

Undefined.

Question 39

Volume of rectangular prism?

Answer 39

Length × Width × Height.

Question 40

Volume of cube?

Answer 40

Side³.

Question 41

Volume of cylinder?

Answer 41

πr²h.

Question 42

Surface area of cube?

Answer 42

6 × side².

Question 43

Should you assume diagram is drawn to scale?

Answer 43

Never unless explicitly stated.

Question 44

If triangle “looks” right-angled but not stated?

Answer 44

Do NOT assume 90°.

Question 45

If two sides equal, can you assume isosceles?

Answer 45

Yes, but only if equality stated.

Question 46

If angles look equal but not stated?

Answer 46

Cannot assume equality.

Question 47

What is biggest geometry DS trap?

Answer 47

Assuming extra constraints not given.

Question 48

When geometry problem complex, what first?

Answer 48

Redraw cleanly and label all known values.

Question 49

If answer choices are far apart?

Answer 49

Estimate before calculating fully.

Question 50

Elite geometry mindset?

Answer 50

Trust formulas. Ignore visual bias. Solve only what’s given.