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Day 11 Triangle Congruence

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Presentation on theme: "Day 11 Triangle Congruence"— Presentation transcript:

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

13

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.

18

19 Example Solve for x:

20 Complete your homework


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