1. 4/27

2. 4/27 Do Now
Essential Question: How can I use proportions to solve for the missing side of a triangle?

3. Agenda Do Now Good Things Recap: Notes:
Triangle Proportionality Theorem
Triangle Angle Bisector Theorem
Notes:
Perpendicular Bisector Theorem

4. Good Things

5. Recap of yesterday…. Triangle Proportionality Theorem
Triangle Bisector Theorem

6. Group Warm Up Find the length of side BC
Find the length of sides BC and CD

7. Perpendicular Bisector Theorem
Altitude – line that connects a vertex to the base and is perpendicular to the base
The altitude creates 2 other right triangles – BDC and ADC
Perpendicular means 90 degrees
Triangle ADC ~ Triangle ACB are similar through AA!
Hint: draw them separately

8. Guided Practice Use corresponding sides to write a proportion with “x”
Cross multiply to solve for x!
Cross multiply to solve for x

9. Guided Practice
Triangle ACB ~ Triangle CDB ~ Triangle ADC

10. Partner Practice
Solve for x

11. Guided Notes!!!
Complete the worksheet using the following BlendSpace link:
guided-notes OR
Each section on the Blendspace matches a section on your paper
This is due at the end of class!
You do NOT need sound for the video – just follow along

12. Congruence Postulates
SSS (Side – Side – Side)
All 3 sides equal

13. Congruence Postulates
SAS (Side – Angle– Side)
Two sides and the included angle are equal

14. Congruence Postulates
ASA (Angle - Side – Angle)
Two angles and the included side are equal.

15. Congruence Postulates
AAS (Angle – Angle – Side)
Two angles and the non-included side are equal.

16. Congruence Postulates
ONLY WORKS FOR RIGHT TRIANGLES******
HL (Hypotenuse – Leg)
Same length of hypotenuse
Same length for one of the other legs

17. Angle Relationships Supplementary angles add up to 180o
These are types of angles that we should already know
Supplementary angles add up to 180o
Hint: form a straight line (also called a straight angle)
Complementary angles add up to 90o
Hint: form a right angle

18. Triangle Sum Theorem
The three interior angles of a triangle always add up to 180 degrees.

19. Exterior Angle Theorem
<A = <C + <D
The exterior angle is equal to the sum of the remote interior angles.

20. Notes: Isosceles Triangles
The base angles of an isosceles triangle are congruent
The legs of an isosceles triangle are congruent

21. Triangle Midsegment Theorem
A midsegment of a triangle is parallel to the base and is half as long as the base.
___ ___
AC || XY
___ ___
XY = ½ * AC

22. Triangle proportionality theorem
In this figure
According to this theorem,
*the arrows in the middle tell us that these lines are parallel
Left Short / Left Long = Right Short / Right Long

23. Triangle Angle Bisector Theorem
A bisector is a line that cuts something in half
If an angle of a triangle is bisected (cut in half), the bisector divides the opposite side of the triangle into two segments that are proportional to the other two sides of the triangle
Bisector
bottom parts of both triangles
hypotenuse of both triangles