1. Triangle Theorems DO NOW 12/15:
Triangle ADB is similar to triangle ABC.
Find the value of x.
(HINT: Use the similarity statement!)
Triangle Theorems
5 m
Agenda
Exit Ticket Corrections
Triangle Inequality Theorem
Hinge Theorem
Debrief
10 m x
Learning Target
I can explain Triangle Inequality Theorem and Hinge Theorem, and relate it to triangle similarity.

2. Exit Ticket

3. SPAGHETTI TIME! (Part I)
Break the stick of spaghetti into ANY three parts.
Measure each of the three parts.
On your sheet, identify each segment as shortest, middle and longest based on the measures.
Did anyone have an equilateral triangle? Isosceles? Scalene?
Add the shortest and middle sides together and compare to the length of the longest. Record your observations.
If possible, use the three segments to make a triangle. Trace the triangle onto a blank/graph piece of paper.
3. Refer back to your answers from #2 above. What was true of the lengths of the 3 sides that could be made into triangles?

4. Triangle Inequality Theorem
In order to form a triangle, the sum of the two smaller sides of a triangle must be greater than the third side.
Ex. AB + BC > AC B A C
**MUST BE IN NOTES!**

5. Spaghetti Time! (Part II)
Once you have your triangle traced on your paper, label the shortest side AB, the middle side BC, and the longest side AC.
Use a protractor to measure angle A, angle B and angle C. Compare the measures.
Which measures are biggest? Which measure is smallest? Which measure is in between?
How is this related to the lengths of the sides?

6. Table of Triangle Parts
Side
Angle
Smallest
Middle
Longest
What relationship do we notice between the location of sides and angles with relative measures?

7. HINge Theorem
The measure of the angles in a triangle are directly related to the lengths of the segments opposite from them.
Ex. If AC > BC > AB, then angle B > angle A > angle C A B C
**MUST BE IN NOTES!**

8. Debrief: Triangle Theorems
How are the sides and angles of triangles related?
How can these two theorems help us when we are trying to determine if two triangles are similar?

9. Special Right Triangles
DO NOW 12/16:
Use a similarity statement and proportions to find the length of y.
Agenda
Embedded Assessment Review
Construct/Bisect Equilateral Triangles ( )
Construct Isosceles Right Triangles ( )
Compare Ratios
Debrief
Learning Target
I can determine the ratios of the sides of all and right triangles.

10. Embedded Assessment review
How far will the judge travel from the start to the 2nd buoy
How far will he be at the 2nd buoy to the finish?
How far is the 2nd buoy from the marker?

11. Construct A Scalene Right Triangle
Draw segment AB of ANY length.
Draw a circle with center point A and radius AB.
Draw another circle with center point B and radius BA.
Label the 2 points of intersection of the two circles C and D.
Draw triangle ABC.
Bisect the triangle by drawing segment CD.
Use the table below to record the side lengths, angle measures and ratios of the two resulting right triangles.
Shorter Leg
Longer Leg
Hypotenuse
Long/Short
Hyp/Long
Hyp/Short
Angle A
Angle M
Angle C

12. Construct an ISOSCELES RIGHT Triangle
Draw segment AB of ANY length.
Draw the perpendicular bisector of AB
Draw circle A with radius greater than half AB
Draw circle B with radius greater than half AB
Label the two points of intersection of the circles C and D
Connect points CD to bisect AD, marking the point of intersection point M
Use the compass to create two congruent segments MA and MB, and connect AB to form a triangle.
Use the table below to record the side lengths, angle measures and ratios of the resulting right triangle.
Leg
Hypotenuse
Leg/Leg
Hyp/Leg
Angle M
Angle A
Angle C

13. Special Right Triangles: 30-60-90
All right triangles with angle measures will have similar side ratios of 1:2:√3 A 2x
60° x
30° B C
x√3
**MUST BE IN NOTES!**

14. Special Right Trangles: 45-45-90
All isosceles right triangles with angle measures of will have side ratios of 1:1:√2 B x x
45°
45° A C
x√2
**MUST BE IN NOTES!**

15. Debrief: Special Right Triangles
How are special right triangles related to similarity?
How is Hinge Theorem and Triangle Inequality related to special right triangles?

16. Trig Ratios DO NOW 12/17: Below are two special right triangles.
Use the ratios to determine the missing sides.
Agenda
Examples 1-6
Right Triangle Ratios in Groups
Examples 7-10
Debrief
Learning Target
I can identify the opposite, adjacent, and hypotenuse of a right triangle, and use the ratios to determine triangle properties.

17. Lesson 25: Trigonometric Ratios

18. Labeling a Right Triangle

19. Group 1

20. Group 2

21. Debrief/Exit Ticket
Are ratios easier/harder than similar triangles? The same? What about it and why?
What are some applications of these ratios in the real world?

22. Simplifying Radicals DO NOW 12/18:
Use the ratios of special right triangles to find the missing variables.
Agenda
Factor Tree/Prime Factorization
Adding and subtracting radicals
Packet Work
Debrief
Learning Target
I can simplify and perform operations with radicals and use radicals to solve problems with right triangles.

23. Simplifying Radicals
A radical is another name for a “root” (like “square root”).
To simplify a radical means to reduce the radicand by factoring until there are no more perfect “roots” under the radical sign.
Ex. √75
Ex. √32x2
**MUST BE IN NOTES!**

24. Operations with Radicals
The key to operating with radicals is to think of them like variables. You can multiply and divide them together, but you can only add or subtract if they are like terms.
Multiplication/Division
√5 × √2 = √10 √12 ÷ √2 = √6
Addition/Subtraction
4√6 + 3√6 = 7√6 8√3 - √75 = 3√3
** No radicals can be in the denominator!** 4 √3

25. Practice With Special Right Triangles and Radicals

26. Problem Set

27. Debrief/Exit Ticket
When are some common situations when we use radicals in trigonometry?
When will simplifying radicals be better than using a decimal?

28. Special Right Triangles Quiz
DO NOW 12/19:
Eat a candy cane and take your quiz.
Agenda
Eat Candy Canes
Take a quiz
Finish your packet/Do extra credit work
Debrief

29. Right Triangles with an Altitude or “Geometric Mean”

30. Special Right Triangles

31. Debrief
Have a safe and relaxing holiday!