1. Day 11 Triangle Congruence

2. Warm-Up #3
Are the triangles congruent? If so, Write the congruence statement. A. B. C. Find the image of V(2, 4) after a translation by the vector < 3, -1> followed by a reflection over the x-axis.

3. HW Check

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

5. 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?

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

7. Examples
Find the value of the missing angle:

8. 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.

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

10. s in which 2 or more sides are
Isosceles Triangles
s in which 2 or more sides are

11. Examples

12. Complete the midsegment worksheet!

13. 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.

14. 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.

15. Example
Solve for x:

16. Complete your homework