1. Day 11 Triangle Congruence

2. Warm-Up #2 ( )
1Are the triangles congruent? If so, Write the congruence statement. If not, write “NO” A. B. 2. Write one net rule for a translation by the vector < 3, -1> followed by a reflection over the x-axis.

3. HW Check

4. Essential Questions (2.11.2014)
How can the Triangle Angle Sum theorem and the Isoceles Triangle Theorem help solve problems involving triangle?
What does the Midsegment Theorem tell me about triangles?

5. Theorem:
is a statement that has been proven on the basis of previously established statements.

6. Triangle sum theorem Take the triangle provided
Label the angles <1, <2, <3
Tear off the angles

7. Compare your work with your partner
Compare your work with your partner. What seems to be true about the three angles of a triangle when they are placed together?
Make a conjecture: What can you say about the sum of the angle measure in a triangle?
An equiangular triangle has three congruent angles. What do you think is true about the angles of an equiangular triangle? Why?
In a right triangle, what is the relationship of the measures of the two acute angles?

8. Triangle-angle sum theorem
The sum of the angles in a triangle is 180.
< 1 + < 2 + < 3 = 180

9. Examples
Find the value of the missing angle:

10. Take the triangles and measure the side lengths.
Use the protractor and measure all the angles.
Make a conjecture about the side lengths of and the angles of this type of triangle.

11. Isosceles Triangle Theorem
If two sides of a triangle are congruent, the angles opposite them are congruent.

12. A in which 2 or more sides are
Isosceles Triangles
A in which 2 or more sides are

14. Examples

15. Complete the midsegment worksheet!

16. Midsegment in Triangles
The mid-segment of a triangle (also called a midline) is a segment joining the midpoints of two sides of a triangle.

17. Mid-segment Theorem Properties
The mid-segment of a triangle joins the midpoints of two sides of a triangle such that it is parallel to the third side of the triangle
2) The mid-segment of a triangle joins the midpoints of two sides of a triangle such that its length is half the length of the third side of the triangle.

19. Example
Solve for x:

20. Complete your homework