Pythagorean Theorem
Today you will need:
Grab a warm-up off the wooden desk and get started!
Goals:
Warm-up #1
| | |
| | |
Simplify. Give exact answers.
Warm-up #2
| |
| |
Find each product.
Simplify. Answer should be exact.
Pythagorean Theorem
The sum of the squares of the legs of a right triangle equals ____________________
___________________________________________.
Represented symbolically: |
https://www.geogebra.org/m/QVBBQeMn Does it always work?
Try it! Find the missing side.
Try it! Find the missing side.KEY!
13
30
15
96
The Hinge Theorem & Pythagorean Theorem
Classify each of the triangles below.
What do you notice about the hypotenuse as the type of triangle changes?
3
4
3
3
4
4
5
The Pythagorean Converse
1681 = 1681
Right
194 < 256
Obtuse
181 > 144
Acute
a =
C = 17
b = 24
a =
Time to Practice!
Pythagorean Theorem
Day 2 - Triples
Today you will need:
Grab a warm-up off the wooden desk and get started!
Goals:
Warm-up #1
Use the given information to find the value of x for each triangle.
Warm-up #1 KEY
Use the given information to find the value of x for each triangle.
X = 10
X = 26
Warm-up #2: Formulas
Warm-up #2
Warm-up #2: KEY
72.25 sqft
159.75 sqm.
91.59 sqin.
530.93 sqyd
368 sqyd
38.85 sqkm
206.5 sqin
189.98 sqm
453.96 sqft
50 sqmm
58.8 sqft
104 sqcm
Use Pythagorean Theorem to complete the table.
KEY!
3
4
5
5
12
13
7
24
25
8
15
17
9
40
41
11
60
61
Use a scale factor to find the new triples!
3, 4, 5
5, 12, 13
7, 24, 25
8, 15, 17
9, 40, 41
11, 60, 61
KEY
3, 4, 5 6, 8, 10 30, 40, 50
5, 12, 13 10, 24, 26 50, 120, 130
7, 24, 25 14, 48, 50 70, 240, 250
8, 15, 17 16, 30, 34 80, 150, 170
9, 40, 41 18, 80, 82 90, 400, 410
11, 60, 61 22, 120, 122 110, 600, 610
12, 16, 20 60, 80, 100
9, 12, 15 15, 20, 25
Find the missing sides using Pythagorean Triples
Triangles are not drawn to scale.
KEY!
Triangles are not drawn to scale.
5
6
13
Find the missing sides using Pythagorean Triples
Triangles are not drawn to scale.
Find the missing sides using Pythagorean Triples
Triangles are not drawn to scale.
15
60
Find the missing sides using Pythagorean Triples
Triangles are not drawn to scale.
Find the missing sides using Pythagorean Triples
Triangles are not drawn to scale.
26
120
41
Find the missing sides using Pythagorean Triples
Triangles are not drawn to scale.
Find the missing sides using Pythagorean Triples
Triangles are not drawn to scale.
100
24
50
2
4
5
10
14
28
8
?
?
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Resources
Mod 5 Standards
G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor:�a. A dilation takes a line not passing through the center of the dilation to a parallel line and leaves a line passing through the center unchanged.�b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures that can be decomposed into triangles.
G.SRT.8 Solve problems involving right triangles�a. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems if one of the two acute angles and a side length is given.
G.SRT.4 Prove and apply theorems about triangles. Theorems include but are not restricted to the following: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures that can be decomposed into triangles.
Tomorrow’s
warm-up
Warm-up
Practice WS
Predict whether the following triangles will be obtuse, acute or right. Then check your answers with the squares.
Check your Answers!
Predict whether the following triangles will be obtuse, acute or right. Then check your answers with the squares.
Warm-up #1
Edit tables to flow better and show relationships…
K*P1=P2
K^2*A1=A2
Warm-up #1
Warm-up #2
Directions: Find the area of each plane figure below.
Warm-up #2