Day 11 Triangle Congruence

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.

HW Check

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

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?

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

Examples Find the value of the missing angle:

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.

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

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

Examples

Complete the midsegment worksheet!

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.

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.

Example Solve for x:

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