WARM-UP — 5 MINUTES

How Tall is Reunion Tower? 🏙️

height = ?

The tower casts a shadow 300 ft long.

A wire from the top to the end of the shadow is 500 ft.

The formula a² + b² = c² is on your REFERENCE CHART!

I DO — PYTHAGOREAN THEOREM WITH DESMOS

Let Desmos Do the Math! 🖩

🔍 Hypotenuse Hunter

c = HYPOTENUSE = the LONGEST side = across from the right angle

Always identify c FIRST!

Context: "A TV at AT&T Stadium is 48 in wide and 36 in tall. What's the diagonal?"

🖩 Desmos Steps

Line 1: a² + b² ~ c² ← tilde, not equals!

Line 2: a = 48

Line 3: b = 36

Line 4: c = ← leave BLANK!

Desmos shows: c = 60 inches!

Finding a LEG instead? Same method! Just leave THAT variable blank.

If c=13, a=5 → leave b blank → Desmos gives b=12!

WE DO — GUIDED PRACTICE

Pythagorean Theorem Practice

🛹 Problem 1: "A ramp at a Dallas skate park: base = 6 ft, height = 8 ft. Find the ramp length."

Label: a = 6 (base), b = 8 (height), c = ? (ramp = hypotenuse) ✅

Desmos: a²+b²~c², a=6, b=8, c= (blank) → c = 10 ft ✅

🪜 Problem 2: "A ladder against a building: base = 5 ft, ladder = 13 ft. How high?"

Label: a = 5 (base), b = ? (height), c = 13 (ladder = hypotenuse) ✅

Desmos Line 1: a² + b² ~ c² ✅

Desmos Line 2: a = ____

Desmos Line 3: b = ____ (leave this ________)

Desmos Line 4: c = ____

Answer: b = ____ ft

I DO / WE DO — TRANSFORMATIONS

Moving Shapes on the Dallas Grid 🗺️

➡️ Translation (Slide)

(x + a, y + b)

"Slide the Cowboys star 3 right and 2 up"
(x+3, y+2)
Point (1,2) → (4,4)

🪞 Reflection (Flip)

y-axis: (−x, y)
x-axis: (x, −y)

"Flip across the Trinity River (y-axis)"
Point (3,5) → (−3,5)

🔄 Rotation 90° CW

(y, −x)

"Turn the Deep Ellum mural 90°"
Point (3,5) → (5,−3)

Quick Memory Trick: Translation = SLIDE (add) | Reflection = FLIP (negate one) | Rotation = TURN (swap & negate)

WE DO — GUIDED PRACTICE

Transformations Practice ✏️

Problem 1: Reflect triangle across the y-axis

Triangle: A(2, 3), B(5, 3), C(2, 7)

Rule for y-axis reflection: (x, y) → (−x, y)

A(2, 3) → A'(−2, 3) ✅

B(5, 3) → B'(____, ____)

C(2, 7) → C'(____, ____)

Problem 2: Translate 4 right, 2 up

Square: (1,1), (1,3), (3,3), (3,1)

Rule: (x+4, y+2)

(1,1) → (5, 3) ✅

(1,3) → (____, ____)

(3,3) → (____, ____)

(3,1) → (____, ____)

🎫 Exit Ticket — Day 4

1. A football field at AT&T Stadium is 100 yards long and 53 yards wide. What is the approximate diagonal distance across the field?

A. 153 yards

B. 113.2 yards

C. 76.5 yards

D. 130 yards

2. Triangle ABC has vertices A(2,3), B(5,3), and C(2,7). If the triangle is reflected across the y-axis, what are the new coordinates of point B?

A. (5, −3)

B. (−5, 3)

C. (−3, 5)

D. (3, −5)

Pythagorean: a²+b²~c² in Desmos | Reflection y-axis: (−x, y)