The Pythagorean Theorem and Its Converse

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Mathematics · Geometry
SP-GEOM-004 · Free to print and use in your classroom · substituteplans.com
Page 2
The Pythagorean Theorem and Its Converse
Mathematics · Geometry · Grades 9-10 · 50 minutes
Time needed
50 minutes (one class period)
Prep
Copy the 2-page worksheet (one per student). Write the theorem and one example on the
board.
Technology
None. A basic calculator is optional.
Student
independence
High. Students work alone with a calculator if available.
Copies to make
One 2-page worksheet per student
Materials
Pencils, Worksheet, Whiteboard or chalkboard, Calculators (optional)
Goal for today: Students will use a² + b² = c² to find missing side lengths and will test whether three side lengths
form a right triangle.
Before the bell
☐ Copy the worksheet, one per student (2 pages).
☐ Write on the board: a² + b² = c² (c is the hypotenuse, the longest side). To find a leg: a² = c² − b². Converse:
if a² + b² = c², the triangle is a right triangle.
☐ Keep the answer key on your desk. You do not need to solve anything yourself.
Say this to start
Good morning! Today’s geometry practice is about the Pythagorean theorem. Students will find missing sides of right
triangles and test whether three lengths make a right triangle. The formula and an example are on the board. A
calculator is helpful but not required, and the answer key tells you which answers to round.
Run of show
Minutes
What you do
What students do
0–5
Take attendance. Hand out the worksheet face down.
Settle in and take out a pencil.
5–12
Read the board example aloud: legs 3 and 4. 3² + 4² = 9 +
16 = 25, so the hypotenuse is √25 = 5. Say that the
hypotenuse is the longest side, across from the right angle.
Follow along and copy the example.
12–32
Tell students to solve questions 1–8 in the work boxes.
Walk around. If a student is unsure whether they are
finding a leg or the hypotenuse, ask: “Is the missing side
the longest side?”
Draw a quick sketch if they like, write the
equation, and solve.
32–40
Tell students to answer questions 9–10 and complete the
Right Triangle Test table.
Square the numbers and decide whether
each set makes a right triangle.
40–46
Read the answers aloud from the key while students check
their work.
Mark each answer and correct mistakes in
a different color if possible.
46–50
Collect all worksheets and stack them for the teacher.
Hand in the worksheet.

SubstitutePlans.com
Mathematics · Geometry
SP-GEOM-004 · Free to print and use in your classroom · substituteplans.com
Page 3
If things go wrong
• If a student gets a leg longer than the hypotenuse, tell them to recheck which side is the longest. The
hypotenuse must be longest.
• If a student has trouble with square roots, allow a calculator or tell them to leave answers as √ numbers and
write an estimate.
• If students ask whether to round, say: round to the nearest tenth when the answer is not a whole number.
• If the room gets loud, remind them this is individual work.
Early finishers
• Find another set of whole numbers that make a right triangle (hint: double 3, 4, 5).
• Write a real-life problem that uses a right triangle and solve it.
• Check whether 20, 21, 29 is a right triangle.
Support and challenge
• Support: Let students use a calculator and complete only questions 1, 2, 3, 6 and 8.
• Challenge: Ask students to find the length of the diagonal of a box that is 3 by 4 by 12 (answer: 13).
Notes for the teacher (you fill this in)
Jot a few lines before you leave. A full Daily Sub Report is in the free Sub Survival Kit at SubstitutePlans.com.
How far the class got / what to pick up next:
Students who were especially helpful:
Anything the teacher should know: