Beth
Menzie
AMSTERDAM HIGH SCHOOL,
AMSTERDAM,
NY

Geometry :
Unit #9 - Similar and Right Triangles :
Lesson #8

Objective:
Students will be able to put their knowledge of special right triangles to work, solving puzzles.

1 Introductory Problems -
5 minutes

When my students arrive for class, I have four Introductory Problems on the board on which I’d like them to work. These problems are designed to help them recall the three types of special triangles that they have learned:

**Pythagorean triplets****30**^{o}, 60^{o}, 90^{o}triangles**45**^{o}, 45^{o}, 90^{o}triangles

When all students have finished filling in the lengths of the missing sides, I ask for volunteers to present the answers to each problem. As we discuss their answers, I plan to ask questions that are designed to help the class recall the last three days’ lessons:

- What is the rule for the side opposite the 30
^{o}angle? - What are some other common Pythagorean triplets?
- When two sides of a triangle are congruent, what square root is associated with this triangle?
- What are the acute angles of an isosceles right triangle?

resources

Introductory Problems.png

https://betterlesson.com/lesson/resource/3133202/introductory-problems-png
2 Puzzle Time -
38 minutes

I ask the students to groups themselves in pairs. As they do I hand out one set of the Activity 1 3x3 puzzle pieces from Special Triangles Puzzle Pieces to each group. The first set is the easiest of the three. The 4x4 set entitled Activity Two is slightly harder, and the set labeled Activity Three is the most challenging.

Each side of a puzzle piece contains some part of a special right triangle. For example, one edge of a square might say 7, 24,____; the students then find another square with the number 25 on one edge and place it adjacent to the 7, 24,____. Once the pieces are matched up correctly, a 3x3 grid will be formed.

I do not give any instructions. I have found that the students figure out what they are supposed to do within a minute or two, and then are off and running. I walk around the room, watching for groups who complete the task. After I check to make sure that their entire square is done correctly, I collect that set and hand out the next set of squares.

If a pair of students completes all three sets of squares and needs something else to do, I hand each student in the pair a blank template and ask each to work on designing his or her own puzzle. I keep these sets from one year to the next. Some students benefit from practicing on more squares, and some students just enjoy the activity and request to do more!

resources

Special Triangles Puzzle Pieces.docx.doc.pdf

https://betterlesson.com/lesson/resource/1986970/special-triangles-puzzle-pieces-pdf
Special Triangles Puzzle Pieces.docx

https://betterlesson.com/lesson/resource/1985774/special-triangles-puzzle-pieces-docx
3 Summary Problems -
3 minutes

With about five minutes to go in the lesson, each student will be given a Ticket out the Door problem to work on. I have included four problems, so that the students will be working on a variety of problems. Each problem is a diagram comprised of set of connecting triangles, on which the students must fill in the missing sides. I will collect the students completed problems as students leave for the day.

resources

Ticket out the Door.docx

https://betterlesson.com/lesson/resource/1985775/ticket-out-the-door-docx
Ticket out the Door.docx.doc.pdf

https://betterlesson.com/lesson/resource/1986969/ticket-out-the-door-pdf