Library

Geometry 8-1 Complete Lesson: The Pythagorean Theorem and Its Converse

By Matt Richardson
Last updated almost 3 years ago
25 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.
1.

Solve It! The squares below fit into groups of three to satisfy the following equation:

area of square 1 + area of square 2 = area of square 3

Write one of these equations.

G.SRT.4
G.SRT.8
A Pythagorean triple is a set of nonzero whole numbers a, b, and c that satisfy the equation below.
Some common Pythagorean triples include:
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25
2.

Problem 1 Got It? The legs of a right triangle have lengths 10 and 24. What is the length of the hypotenuse? Enter only a number.

3.

Problem 1 Got It? Do the side lengths in the previous item form a Pythagorean triple? Explain.

G.SRT.4
4.

Problem 2 Got It?

G.SRT.8
5.

Problem 3 Got It?

G.SRT.8
6.

Problem 4 Got It? A triangle has side lengths 16, 48, and 50. Is the triangle a right triangle? Explain.

G.SRT.4
G.SRT.8
7.

Problem 5 Got It?

G.SRT.4
G.SRT.8
8.
G.SRT.8
9.
G.SRT.8
10.
G.SRT.8
11.
G.SRT.8
13.

Error Analysis: A triangle has side lengths 16, 34, and 30. Your friend says it is not a right triangle. Look at your friend's work and describe the error.

G.SRT.8
14.

Review Lesson 7-5: â–³ABC has side lengths AB = 8, BC = 9, and AC = 10.
1. Sketch â–³ABC. Label the vertices and side lengths.
2. Sketch the bisector of ∠A.
3. Find and label the lengths of the segments formed on segment BC by the bisector of ∠A.

G.SRT.4
G.SRT.5
15.

Preview Lesson 8-2: Simplify the expression.

16.

Preview Lesson 8-2: Simplify the expression.

17.

Preview Lesson 8-2: Simplify the expression.

18.

Enter only a number.

19.

Enter only a number.

20.

Enter only a number.

21.

Enter only a number.

22.

Use Your Vocabulary: The hypotenuse is the longest side in a right triangle.

23.

Use Your Vocabulary: Classify each statement as True or False.

  • True
  • False
  • The hypotenuse is the longest side in a right triangle.
  • The hypotenuse of a right triangle can be any one of the three sides.
  • In a triangle with side lengths 3, 4, and 5, one of the legs measures 4.
24.

Use Your Vocabulary: Classify each statement as True or False.

  • True
  • False
  • One leg of the triangle has length 9 cm.
  • The hypotenuse of the triangle has length 12 cm.
  • The side lengths of the triangle form a Pythagorean triple.
25.

Reflection: Math Success

G.SRT.4
G.SRT.8