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Name _______________________________________ Date __________________ Class __________________ Geometry Section 4.2 Classifying Triangles Classification Description Example triangle that has three acute angles triangle that has three congruent acute angles triangle that has one right angle triangle that has one obtuse angle triangle with three congruent sides triangle that has at least two congruent sides triangle that has no congruent sides Classify each triangle by its angle measures. (Note: Some triangles may belong to more than one class.) 1. ABD ________________________ 2. ADC ________________________ 3. BCD ________________________ Classify each triangle by its side lengths. (Note: Some triangles may belong to more than one class.) 4. GIJ ________________________ 5. HIJ ________________________ 6. GHJ ________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry Name _______________________________________ Date __________________ Class __________________ Find the side lengths of each triangle. 7. 8. 9. Classify the triangle. 10. What type of triangle is F isosceles acute A acute, isosceles G isosceles obtuse B acute, scalene H scalene acute C obtuse, isosceles J scalene obtuse D obtuse, scalene ABC? Decide if triangles are congruent by using the distance formula for diagonal sides. Find the measure of each segment. Round answers to the nearest hundredth. Use the information to determine if the triangles are congruent. Show all length calculations!! RS = _______ RQ = _______ QS = ________ WY = ________ XY = ________ WX = ________ Are these triangles congruent to each other?_____ if yes, then RSQ Name _______________________________________ Date __________________ Class __________________ 4.9 Isosceles and Equilateral Triangles Theorem Examples Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite the sides are congruent. If RT RS, then T S. Converse of Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent. If N M, then LN LM. Equilateral Triangle Corollary If a triangle is equilateral, then it is equiangular. (equilateral equiangular ) Equiangular Triangle Corollary If a triangle is equiangular, then it is equilateral. (equiangular equilateral ) If A B C, then AB BC CA . Find each value. 1. mD ________ 2. GI ________ 3. mL ________ 4. RQ ________ Name _______________________________________ Date __________________ Class __________________ 5. mU ________ 6. t ________ 7. What is the value of x in the figure? 8. What is the value of x in the figure? 9. What is the value of x in the figure? 10. What is the value of x in the figure? 11. What is the value of x? x = _______ 12. What is the value of x in the figure?