Triangle Blueprints Slides
Triangle Blueprints
Special Right Triangle Mastery
Sheet No. 00
The 45-45-90 Triangle
Sheet 01
Internal Ratio:
x : x : x√2
- Legs are equal in length.
- Hypotenuse = Leg × √2.
x x x√2 45° 45°
Example Practice
Practice 01
Draft Specification:
If a leg is 12, calculate the hypotenuse.
Protocol Solution:
12 × √2 = 12√2
12 12 ?
The 30-60-90 Triangle
Sheet 02
Internal Ratio:
x : x√3 : 2x
Short Leg (x) Opposite 30°
Long Leg (x√3) Opposite 60°
Hypotenuse (2x) Opposite 90°
x x√3 2x 30° 60°
Example Practice
Practice 02
Short Leg = 5
Hypotenuse: 5 × 2 = 10
Long Leg: 5√3
5 ? ? 30°
Blueprint Summary
45-45-90 Ratio
Leg x
Hypotenuse x√2
Two equal legs. Diagonal of a square.
30-60-90 Ratio
Short Leg x
Long Leg x√3
Hypotenuse 2x
Double the short leg for the hypotenuse.
Project Completed
Triangle Draftsman Worksheet
Triangle Draftsman Guide
Special Right Triangles • Step-by-Step Practice
Name:
Date:
1
Section 01: 45-45-90 Blueprint
x x x√2
Protocol Rules:
• Both legs are equal (x). Hypotenuse = Leg × √2.
Draft 01: Find the hypotenuse if the leg is 15.
Step 1: Write Ratio (x : x : x√2)
Step 2: Calculate (15 × √2)
Final Value
Draft 02: Find the leg if the hypotenuse is 10√2.
Step 1: Set equation (x√2 = 10√2)
Step 2: Solve for x
Final Value
2
Section 02: 30-60-90 Blueprint
x x√3 2x
Protocol Rules:
1. Short Leg (x) is across from 30°. Hypotenuse = 2x. Long Leg = x√3.
Draft 03: Short Leg is 7. Find all other sides.
Step 1: Identify Short Leg (x = 7)
Step 2: Hypotenuse (2x)
Step 3: Long Leg (x√3)
7 ? ?
Draft 04: Hypotenuse is 18. Find the legs.
Step 1: Solve for Short Leg (2x = 18)
Step 2: Calculate Long Leg (x√3)
SHORT LEG:
LONG LEG:
Triangle Master Series • Vol 1 v2.2 • Blueprints Practice
Triangle Inspector Key
Inspector Answer Key
Triangle Blueprints • Solutions Guide
Teacher Only
Section 01 Solutions
Draft 01: Leg = 15
Step Logic:
1. Identify x = 15
2. Calculation: 15 * √2
15√2
Draft 02: Hypotenuse = 10√2
Step Logic:
1. Equation: x√2 = 10√2
2. Resolution: x = 10
10
Section 02 Solutions
Draft 03: Short Leg = 7
Step Logic:
1. x = 7
2. Hypotenuse: 2x = 14
3. Long Leg: x√3 = 7√3
HYP: 14
LONG: 7√3
Draft 04: Hypotenuse = 18
Step Logic:
1. 2x = 18 -> x = 9
2. Long Leg: x√3 = 9√3
SHORT: 9
LONG: 9√3
Ensure students show all logic steps clearly for full credit.
Triangle Master Key v2.1
