Lesson 5 • 40 min read
Geometry & Statistics
1Types of Angles
Acute Angle
Measures less than 90°
Examples: 30°, 45°, 60°, 89°
Right Angle
Measures exactly 90°
Forms an "L" shape, marked with a small square
Obtuse Angle
Measures more than 90° but less than 180°
Examples: 91°, 120°, 150°, 179°
Straight Angle
Measures exactly 180°
Forms a straight line
Quick Reference
Acute
0° - 89°
Right
90°
Obtuse
91° - 179°
Straight
180°
2Angle Relationships
Complementary Angles
Two angles that add up to 90°
∠A + ∠B = 90°
If ∠A = 30°
Then ∠B = 60°
If ∠A = 45°
Then ∠B = 45°
Supplementary Angles
Two angles that add up to 180°
∠A + ∠B = 180°
If ∠A = 120°
Then ∠B = 60°
If ∠A = 90°
Then ∠B = 90°
Vertical Angles
Opposite angles formed when two lines intersect. They are always equal!
When two lines cross:
∠1 = ∠3 and ∠2 = ∠4
Vertical angles are congruent (equal measure)
Problem Solving Example
If two angles are supplementary and one measures 65°, find the other.
∠A + ∠B = 180°
65° + ∠B = 180°
∠B = 180° - 65°
∠B = 115°
3Triangle Classification
By Sides
Equilateral Triangle
All 3 sides are equal
Also has 3 equal angles (60° each)
Isosceles Triangle
2 sides are equal
Has 2 equal base angles
Scalene Triangle
No sides are equal
All 3 angles are different
By Angles
Acute Triangle
All 3 angles are less than 90°
Right Triangle
Has exactly one 90° angle
The other two angles add to 90°
Obtuse Triangle
Has one angle greater than 90°
Only one obtuse angle is possible
Triangle Angle Sum Property
The sum of all angles in any triangle equals 180°
∠A + ∠B + ∠C = 180°
If ∠A = 60° and ∠B = 70°
Then ∠C = 180° - 60° - 70° = 50°
4Measures of Central Tendency
These are ways to find a "typical" or "central" value in a set of data.
Mean (Average)
Add all values and divide by the number of values.
Mean = (Sum of all values) ÷ (Number of values)
Example: Data set: 5, 7, 8, 10, 10
Sum = 5 + 7 + 8 + 10 + 10 = 40
Count = 5 values
Mean = 40 ÷ 5 = 8
Median (Middle)
The middle value when data is arranged in order.
Odd number of values:
Data: 5, 7, 8, 10, 10 (already in order)
Median = 8 (the middle one)
Even number of values:
Data: 3, 5, 7, 9 (average of two middle values)
Median = (5 + 7) ÷ 2 = 6
Mode (Most Frequent)
The value that appears most often.
Example 1: Data: 5, 7, 8, 10, 10
Mode = 10 (appears twice)
Example 2: Data: 2, 3, 3, 5, 5, 7
Mode = 3 and 5 (bimodal - two modes)
Example 3: Data: 1, 2, 3, 4, 5
No mode (all appear once)
When to Use Each
| Measure | Best Used When... |
|---|---|
| Mean | Data has no extreme outliers |
| Median | Data has outliers (extreme values) |
| Mode | Finding most common category or value |