Geometry Chapter 5 Review Relationships Within Triangles. 1. A midsegment of a triangle is a segment that connects the of two sides.

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Geometry Chapter 5 Review Relationships Within Triangles Name: SECTION 5.1: Midsegments of Triangles 1. A midsegment of a triangle is a segment that connects the of two sides.

1 Geometry Chapter 5 Review Relationships Within Triangles Name: SECTION 5.1: Midsegments of Triangles 1. A midsegment of a triangle is a segment that connects the of two sides. A midsegment is to the third side and its length. 2. X is the midpoint of UV. Y is the midpoint of UW. 3. Find the value of x. If VW = 110, find XY. 4. B is the midpoint of and D is the midpoint of Solve for x, given BD = 6x + 1 and AE = 13x 7. C B D A E 5. Given the perimeter of FGE is 35 find the value of x if AB = 2x +16, CB = 8x+6 and AC = 4x Solve for x.

2 SECTION 5.2: Bisectors in Triangles 7. A point is on the perpendicular bisector of a segment if and only if it is from the endpoints of that segment. A point is on the angle bisector of an angle if and only if it is from the of the angle. 8. From the information given in the picture, how is 9. Find JM. AC related to BD? Find AB Use the figure below to answer the following questions: a. What is the measure of XV? b. What is the measure of XY? 12. Q is equidistant from the sides of Find The diagram is not to scale. c. Classify WXZ by its sides. T Q S (4x + 3) (8x 5) R

SECTION 5.3: Congruent Lines, Medians, and Altitudes 13. The medians of a triangle intersect at the. The circumcenter of a triangle is equidistant from the of the triangle.

3 SECTION 5.3: Congruent Lines, Medians, and Altitudes 13. The medians of a triangle intersect at the. The circumcenter of a triangle is equidistant from the of the triangle. An altitude of a triangle starts at a and is to the opposite side. The incenter is the point of concurrency for the of a triangle. 14. Determine whether AB is a perpendicular bisector, altitude, angle bisector, median, or none. a. b. 15. Find the coordinates of the circle circumscribed about the given triangle. 16. Find the coordinates of the circumcenter and the orthocenter of the traingle. 17. Sketch and label the medians of the triangle below. What is the point of concurrency called?

4 18. Create CUB with vertices C (4, 6), U(4, -2) and B(-6, 6) on the graph above. a. What are the coordinates of the circumcenter? b. What are the coordinates of the orthocenter? 19. In the diagram below: AF is a(n). BD is a(n). CE is a(n). SECTION 5.4: Inverse, Contrapositives, and Indirect Reasoning 20. Consider the conditional statement: If it is snowing, then it is cold outside. What is the converse of the conditional (from Chapter 2)? What is the inverse of the conditional? What is the contrapositive of the conditional? Circle which are true: conditional, converse, negation, inverse, contrapositive 21. Write the first step for the indirect proof of the following Given: LMN Prove: LMN has at most 1 right angle.

5 22. Select the two statements that contradict eachother. SECTION 5.5: Inequalities in Triangles 23. Name the largest angle of The diagram is not to scale. a. Two angles are the same size and smaller than the third. b. c. d. C 5 6 A 7 B 24. List the angles in order from smallest to largest. 25. List the sides in order from largest to smallest. 26. Which segment is the largest? Which segment is the smallest? 27. Is it possible to have a triangle with sides of the given lengths? 2cm, 3cm, 6cm 4in, 4in, 8in 4.5ft, 6ft, 11ft

6 28. Which three lengths could not be the lengths of the sides of a triangle? a. 9 cm, 22 cm, 15 cm c. 12 cm, 5 cm, 17 cm b. 21 cm, 17 cm, 6 cm d. 10 cm, 15 cm, 24 cm 29. A triangle has the following angle measures, list the sides in order of largest to smallest. m<t = 4x + 15 m<r = 7x + 4 m<s = 5x and List the sides of in order from smallest to largest. 31. Where do all medians meet (in, on, out)? What is this called? 32. Where do all angle bisectors meet (in, on, out)? What is this called? 33. Where do all perpendicular bisectors meet (in, on, out)? What is this called? 34. Where do all altitudes meet (in, on, out)? What is this called?

7 35. The measure of the exterior angle is EQUAL, GREATER THAN, or LESS THAN the sum of the remote interior angles? 36. A triangle has sides 2 and 8 inches. Write an inequality to show the range of values for the third side. 37. Two sides of a triangle have lengths 32 and 21. Write an inequality statement that describes the values for the possible lengths of the third side. 38. Respond to the following questions with always, sometimes, never. a. A true statement has a false negation. b. An altitude of a triangle is also an angle bisector. c. The medians of an acute triangle meet inside the triangle. d. The midsegment of a triangle is congruent to the side it is parallel to. e. The angle bisectors of a triangle are concurrent at one point.

Name Period 10/22 11/1 10/31 11/1. Chapter 4 Section 1 and 2: Classifying Triangles and Interior and Exterior Angle Theorem

Name Period 10/22 11/1 10/31 11/1. Chapter 4 Section 1 and 2: Classifying Triangles and Interior and Exterior Angle Theorem Name Period 10/22 11/1 Vocabulary Terms: Acute Triangle Right Triangle Obtuse Triangle Scalene Isosceles Equilateral Equiangular Interior Angle Exterior Angle 10/22 Classify and Triangle Angle Theorems