Unit 2 Triangles Part 1

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1 Graded Learning Targets LT 2.1 I can Unit 2 Triangles Part 1 Supporting Learning Targets I can justify, using a formal proof, that the three angles in a triangle add up to 180. I can justify whether or not three sides will create a triangle. I can explain and use the relationship between the side lengths and angle measures of a triangle. I can construct the three midsegments of a triangle and explain the results. I can classify and define different types of If time: I can construct the points of concurrency (incenter, circumcenter, orthocenter, and centroid). Book 4.1, 4.3, 5.4, 1.5, 3.7, 3.8 LT 2.2 I can equilateral and isosceles I can construct an equilateral triangle. I can justify (prove) algebraically that the angles in an equilateral triangle are each 60. I can identify the base angles of an isosceles triangle. I can construct an isosceles triangle. I can compare and contrast equilateral and isosceles 3.1, 4.1, 4.2, 4.8 LT 2.3 I can congruent I can identify corresponding parts of I can explain why triangles are or are not congruent. I can explain which congruency shortcuts work and which ones don t. I can justify (prove) by contradiction that AAA and SSA are not congruency shortcuts. I can justify, using a flowchart, two-column, and paragraph proof, that two triangles are congruent using congruency shortcuts. I can justify, using any proof, that corresponding parts of congruent triangles are also congruent (CPCTC). 4.4, 4.5, 4.6, 4.7

2 LT 2.4 I can apply the Pythagorean Theorem and its converse to solve problems and logically justify LT 2.5 I can apply the special right triangles to solve problems and logically justify LT 2.6 I can use coordinate geometry to translate, reflect, and rotate triangles and analyze the result. I can apply the Pythagorean Theorem to real world problems. I can find the converse, inverse, and contrapositive of a statement. I can determine whether a triangle is a right triangle. I can apply the isosceles right triangles to solve and logically justify I can apply the I can translate, reflect, and rotate (90, 180, 270 ) triangles on a coordinate plane using ordered pair rules. I can prove that translations, reflections, and rotations of triangles are congruent using the distance formula and congruency shortcuts. I can create the ordered pair rule for a translation, reflection, and rotation of a triangle on a coordinate plane. 9.1, 9.2, , 7.2, 9.5 Unit 2 Conjectures LT 2.1 I can Triangle Sum Conjecture: The sum of the measures of the angles in every triangle is. Third Angle Conjecture: If two angles of one triangle are equal in measure to two angles of another triangle, then the third angle in each triangle. Triangle Inequality Conjecture: The sum of the lengths of any two sides of a triangle is than the length of the third side. Side-Angle Inequality Conjecture: In a triangle, if one side is longer than another side, then the angle opposite the longer side is.

3 Triangle Exterior Angle Conjecture: The measure of an exterior angle of a triangle is the sum of. Three Midsegments Conjecture: The three midsegments of a triangle divide it into. Triangle Midsegment Conjecture: A midsegment of a triangle is to the third side and the length of. If time: Perpendicular Bisector Concurrency Conjecture: The three perpendicular bisectors of a triangle. Angle Bisector Concurrency Conjecture: The three angle bisectors of a triangle. Circumcenter Conjecture: The circumcenter of a triangle is. Incenter Conjecture: The incenter of a triangle is. Altitude Concurrency Conjecture: The three altitudes (or the lines containing the altitudes) of a triangle. Median Concurrency Conjecture: The three medians of a triangle. Center of Gravity Conjecture: The of a triangle is the center of gravity of the triangular region. LT 2.2 I can equilateral and isosceles Equilateral/Equiangular Triangle Conjecture: Every equilateral triangle is, and, conversely, every equiangular triangle is. Vertex Angle Bisector Conjecture: In an isosceles triangle, the bisector of the vertex angle is also a. Isosceles Triangle Conjecture: If a triangle is isosceles, then. Converse of the Isosceles Triangle Conjecture: If a triangle has two congruent angles, then.

4 LT 2.3 I can congruent SSS Congruence Conjecture: If the three sides of one triangle are congruent to the three sides of another triangle, then. SAS Congruence Conjecture: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then. ASA Congruence Conjecture: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then. AAS (SAA) Congruence Conjecture: If two angles and a non-included side of one triangle are congruent to the corresponding angles and side of another triangle, then. LT 2.4 I can apply the Pythagorean Theorem and its converse to and logically justify The Pythagorean Theorem: In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. If a and b are the lengths of the legs, and c is the length of the hypotenuse, then. Converse of the Pythagorean Theorem: If the lengths of the three sides of a triangle satisfy the Pythagorean equation, then the triangle is a. LT 2.5 I can apply the special right triangles to and logically justify my results. Isosceles Right Triangle Conjecture: In an isosceles right triangle, if the legs have length l, then the hypotenuse has length.

5 Triangle Conjecture: In a triangle, if the shorter leg has length a, then the longer leg has length and the hypotenuse has length. LT 2.6 I can use coordinate geometry to translate, reflect, and rotate triangles and analyze the result. Distance Formula: The distance between points A(x 1, y 1 ) and B(x 2,y 2 ) is given by (AB) 2 = ( ) 2 + ( ) 2 or AB = Ordered Pair Rules: Translation right h up k: Clockwise rotation of 90 about the origin: Clockwise rotation of 180 about the origin: Clockwise rotation of 270 about the origin: Counterclockwise rotation of 90 about the origin: Counterclockwise rotation of 180 about the origin: Counterclockwise rotation of 270 about the origin: Reflection across the x-axis: Reflection across the y-axis: Reflection across the line y = x:

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