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NAME:____________________________________ DATE: 02/12 ASSIGNMENT: Angle Relationships in Triangles DIRECTIONS: We know that a RIGHT triangle contains one RIGHT angle. If we know that all three angles must add to 180º, then we also know that the other two non-right angles are acute. They must add to 90º, thus each one must be less than 90º. In an EQUIANGULAR triangle, all angles must be EQUAL and, since this is a triangle, SUM to 180º. There is only one number that satisfies this requirement. 60º. Therefore, every angle in an EQUIANGULAR triangle must be 60º. If we have two triangles where two of their angles are congruent to two angles of the other triangle, then the third angles are congruent. For example, if we have two triangles, and they each have two angles measuring 40º and 60º, we know that the third angle MUST BE 80º for those triangles’ angles to add to 180º. 1.) If Angle P = 46º and Angle T = 4x − 6, what does “x” have to equal? " x = ______ 2.) " " " " " " Find Angle NKM. " " " " " " Angle NKM = _________ " " " " " " Find Angle JLK. " " " " " " Angle JLK = __________ 3.) The angles of a triangle are in the ratio of 1:2:3. Find the values of the angles. Smallest Angle = ______"Middle Angle = _______" Largest Angle = ________ 4.)" " " " " " " " In the diagram to the left, m∠A = 80º, m∠B = xº, and m∠ACD = 3xº. Find m∠ACB. " " " " " " " " " m∠ACB = ________ ASSIGNMENT: Congruent Triangles DIRECTIONS: Congruent Triangles have congruent corresponding sides and angles. “Corresponding” means that those sides and angles would “match up” if the shapes were stacked on top of one another. Congruent triangles are congruent if and only if their sides and angles are congruent. When naming congruent triangles, you have to name the corresponding vertices in the same order. For example: With these triangles, the following parts are congruent. Angle A = Angle I; Angle C = Angle G Angle B = Angle H Side AB = Side IH; Side BC = Side HG Side AC = Side IG Also, we could say that Triangle ABC = Triangle IHG; Triangle BCA = Triangle HGI Triangle CAB = Triangle GIH HOWEVER, this out-of-order sequence is incorrect. Triangle ABC ≠ Triangle GIH 5.) ⧍EFH ≅ ⧍GFH Find “x.” x = __________ Find m∠GFH. m∠GFH = __________ 6.) ⧍SGE and ⧍KPM are congruent. Name all the corresponding vertices and sides. 7.) ⧍SDF and ⧍XCV are congruent. If SD = 5x − 7 and XC = 13, what is the value of “x” and Side SD? x = ________ Side SD = _________ Answers: 1.) x = 13 2.) Angle NKM = 44º; 3.) 30º; 60º; 90º 4.) 60º 5.) x = 17 6.) tutorials 7.) x = 4 Angle JLK = 78º