# CST Geometry Practice Problems

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1 ST Geometry Practice Problems. Which of the following best describes deductive reasoning? using logic to draw conclusions based on accepted statements accepting the meaning of a term without definition defining mathematical terms to correspond with physical objects inferring a general truth by eamining a number of specific eamples. Jane sees three girls with blond hair wearing jeans, she concludes that all blonds wear jeans. This is an eample of what kind of reasoning? deductive reasoning indirect proof countereample inductive reasoning 3. In the diagram below, 4 l m 3 4 Which of the following conclusions does not have to be true? and are supplementary angles. Line l is parallel to line m Theorem: triangle has at most one obtuse angle. Eduardo is proving the theorem above by contradiction. He began by assuming that in, and are both obtuse. Which theorem will Eduardo use to reach a contradiction? If two angles of a triangle are equal, the sides opposite the angles are equal. If two supplementary angles are equal, the angles each measure 90. The largest angle in a triangle is opposite the longest side. The sum of the measures of the angles of a triangle is Use the proof to answer the question below. Statement Reason. WZ = ZY;. Given X is the midpoint of WY. WX = YX efinition of Midpoint 3. ZX = ZX 3. Refleive Property 4. WZX YZX 4.? What reason can be used to prove that the triangles are congruent? S S SS SSS 6. Two lines in a plane always intersect in eactly one point. Which of the following best describes a countereample to the assertion above? coplanar lines parallel lines perpendicular lines intersecting lines 7. Which figure can serve as a countereample to the conjecture below? If one pair of opposite sides of a quadrilateral is parallel, then the quadrilateral is a parallelogram. rectangle rhombus square trapezoid 8. Given: TRP is an isosceles trapezoid with diagonals RP and T. Which of the following must be true? Given: WZ ZY; X is the midpoint of WY. Prove: WZX YZX RP T RP T RP T RP bisects T W X Z Y

2 9. Which triangles must be similar? two obtuse triangles two scalene triangles with congruent bases two right triangles two isosceles triangles with congruent verte angles n n 0. Which of the following facts would be sufficient to prove that triangles E and are similar? In the figure below, what is the largest possible value for? and are congruent. E is a right angle. E and are parallel. and E are congruent. Parallelogram is shown below. E In the accompanying diagram, parallel lines l and m are cut by transversal t. t E l Which pair of triangles can be established to be congruent to prove that? and E and E and E and E m. If and XYZ are two triangles such that = XY, which of the following would be sufficient to prove the YZ triangles are similar? X Y Z X Y 3. In the figure below, n is a whole number. What is the smallest possible value for n? Which statement about angles and must be true?. is the complement of. is the supplement of. and are right angles. 6. Quadrilateral is a parallelogram. If adjacent angles are congruent, which statement must be true? Quadrilateral is a square. Quadrilateral is a rhombus. Quadrilateral is a rectangle. Quadrilateral is an isosceles trapezoid.

3 7. Figure is a kite. 0. What is the area, in square units, of the trapezoid shown below? (0, 5) y (8, 5) 0 cm 7 cm 8 cm 6 cm 5 cm 8 cm 0 cm 7 cm 0 (, 0) What is the area of figure, in square centimeters? The diameter of a circle is 8cm, what is its circumference? 8 cm 4 π cm 6 π cm 8 π cm 4 π cm 9. The rectangle shown below has length 0 meters and width 0 meters The perimeters of two squares are in a ratio of 4 to 9. What is the ratio between the areas of the two squares? to 3 4 to 9 6 to 7 6 to 8. model car is /4 the size of the original. It is made of the same materials as the original car. What would the ratio of their weights be? /6 /8 /64 4/6 3. Two angles of a triangle have measures of 55 and 65. Which of the following could not be a measure of an eterior angle of the triangle? If four triangles are removed from the rectangle as shown, what will be the area of the remaining figure? 4. The sum of the interior angles of a polygon is the same as the sum of its eterior angles. What type of polygon is it? quadrilateral heagon octagon decagon 36 m 4 68 m 8

4 5. What is m 8. diagram from a proof of the Pythagorean Theorem is pictured below. a b If the measure of an eterior angle of a regular polygon is 0, how many sides does the polygon have? What is m? Which statement would not be used in the proof of the Pythagorean Theorem? The area of a triangle equals ab. The four right triangles are congruent. The area of the inner square is equal to half of the area of the larger square. The area of the larger square is equal to the sum of the areas of the smaller square and the four congruent triangles. 9. right triangle s hypotenuse has length 5. If one leg has length, what is the length of the other leg? c c 30. Marsha is using a straightedge and compass to do the construction shown below.. P Which best describes the construction Marsha is doing? a line through P parallel to line l a line through P intersecting line l a line through P congruent to line l a line through P perpendicular to line l

5 3. Given : angle 33. In the figure below, if sin = 3 5, what are cos and tan? What is the first step in constructing the angle bisector of angle? raw ray. raw a line segment connecting points and. From points and, draw equal arcs that intersect at. From point, draw an arc that intersects the sides of the angle at points and. 3. Figure O is a parallelogram. 5 cos = and tan = 3 cos = and tan cos = and tan = (a,b) (a+c,b) 3 3 cos = and tan = In the figure below, sin = 0.7 O (c,0) What are the coordinates of the point of intersection of the diagonals? a b c b a c b a c a b What is the length of?

6 35. In the accompanying diagram, m = 3 and = 0. Which equation could be used to find in? = 0sin3 = 0cos3 = 0tan 3 = 3 0 cos The diagram shows an 8-foot ladder leaning against a wall. The ladder makes a 53 angle with the wall. Which is the closest to the distance up the wall the ladder reaches? 38. square is circumscribed about a circle. What is the ration of the area of the circle to the area of the square? The vertices of are (,), (3,4), and (,3). If is translated unit down and 3 units to the left to create EF, what are the coordinates of the vertices of EF? (0,), E(,), F(,) (0, ), E(3,0), F(, ) (.), E(0,3), F(,0) (,0), E(0,3), F(,) 40. If triangle is rotated 80 degrees about the origin, what are the coordinates of? sin cos tan ft 53? 3. ft 4.8 ft 6.4 ft 9.6 ft 37. If a= 3 3 in the right triangle below, what is the value of b? a ( 5, 4) ( 5, 4) ( 4, 5) ( 4, 5) b 30 c

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