Honors Geometry Semester 1 Review Problems CHAPTER 1 1) Find the union or the intersection: a) AE HE = ∩ b) AE HE = ∪ c) HT TE = ∩ d) ML LE = ∩ e) EM ET = ∪ f) AE TH = ∪ 2) ∠CAT is a right angle. Find m∠CAS. 3) Find the measure between the hands of a clock at 4:42. 4) State the restrictions on x. 5) What logical conclusion can be drawn using all of the information below? If Bob doesn’t butter bread, then Sam sings songs. If Melanie doesn’t make muffins, then Albert acts antisocial. If Frank fly fishes, then Rene runs races. If Melanie makes muffins, then Sam doesn’t sing songs. If Bob butters bread, then Rene doesn’t run races. 6) Find the measure(s) of ∠CAT. C A T S 43 9'37" ° 2 8 2x + 10 C A S T (174 – x)° (x 2 )° M S E H T A L
3) Find the measure between the hands of a clock at 4:42. 4) State the restrictions on x. 5) What logical conclusion can be drawn using all of the information below? If Bob doesn’t butter bread, then Sam sings songs. If Melanie doesn’t make muffins, then Albert acts antisocial. If Frank fly fishes, then Rene runs races. If Melanie makes muffins, then Sam doesn’t sing songs. If Bob butters bread, then Rene doesn’t run races. 6) Find the measure(s) of ∠CAT.
C
A T
S
43 9'37"°
2 8
2x + 10
C A S
T
(174 – x)° (x2)°
M
S
E H T A
L
7) Convert 27°44’30” to degrees (exact answer). 8) Convert 98.38° to degrees/minutes/seconds. CHAPTER 2
9) Solve for y in terms of x. 10) The ratio of two complementary angles is 8 to 7. Find the measure of the larger angle.
11) Half the supplement of an angle is 7 less than 6 times the complement of the supplement. Find the angle. 12) The supplement of an angle plus the trisected complement of 30 ° is three times the complement of the angle. Find the supplement of the complement.
CHAPTER 3
13) The perimeter of ∆BAG is 43. AG = 16, AB = x + 4, BG = 2x + 2. By solving for x, determine whether ∆BAG is scalene, isosceles, or equilateral.
x + 15 y – 3x
14) The lengths of the base and a leg of an isosceles triangle are in the ratio of 3:2. The perimeter of the triangle is 105. Find the length of the base.
15) Given: EF ED> State both restrictions on x. ________< x < _________
CHAPTER 4.1 – 4.4
16) A is the midpoint ofCT . Find the coordinates of T.
CHAPTER 4.5 – 5.3
17) Find x. 18) Find the restrictions on x.
D
E
F (3x – 10)° (x – 2)°
CT
A(-3, 4)
(4, 7)
x°
96°
138°
(3x + 5)°
(x + 18)°
19) Find the slope of the median and altitude from vertex L in ∆LCD. L (2, -5) C (6, -2) D (8, 7) 20) Show that a||b or a||b, which ever the case may be.
CHAPTER 5.4 – 5.7
21) Give the most specific name of parallelogram ABCD
AE = 2x – y, BE = 6 + 2y, DE = x + y, EC = 18 ∠1 = (10x)° 22) Is this a parallelogram based on the given information?
PG ||AR , ∠1 = (50 + 5y)°, ∠2 = (-11x + y4
5)°,
∠3 = (2x + 10y)°, ∠4 = (-2x + 5y)°
(72 – y)°
(3y – 12)° (5y + 20)°
b
a
A B
C
E1
D
P G
R
1 2
34
A
23) Based on the information given identify the quadrilateral as specifically as possible. a) b) c)
CHAPTER 7
24) Find the measure of ∠1. 25) Find the name of the regular polygon that has a measure of 15° for each exterior angle. 26) Find the sum of the interior angles and the number of diagonals in a dodecagon. 27) Find the value of x. 28) The measure of an angle of an equiangular polygon exceeds four times the measure of one
of the polygon’s exterior angles by 30°. What is the name of the polygon? 29) How many sides does a polygon have if it has 189 diagonals?
40° (2x + 50)°
(x + 50)°
1
x
40°
ASN PRACTICE! Answer Always, Sometimes, or Never. _____ 1. Supplementary angles are congruent. _____ 2. The complement of an angle is congruent to its supplement. _____ 3. The supplement of the complement of an angle is obtuse. _____ 4. If two angles are complementary, they are each acute. _____ 5. Vertical angles are complementary. _____ 6. The relation “is perpendicular to” is transitive, that is, if a b⊥ and b c⊥ , then a c⊥ . _____ 7. An obtuse triangle has 3 obtuse angles.
_____ 8. A right triangle is isosceles. _____ 9. If a median of a triangle is also an altitude, then it is also an angle bisector.
_____ 10. If AB BC≅ in ∆ABC, then ∠BAC ≅ ∠ABC.
_____ 11. If AB AC≅ in ∆ABC, then ∠BCA ≅ ∠ABC. _____ 12. If all three angles in one triangle are congruent to all three angles in another triangle, then the triangles are congruent. _____ 13. The median of a triangle is also an angle bisector. _____ 14. A right triangle is equiangular. _____ 15. An obtuse triangle has 2 obtuse angles. _____ 16. An angle bisector of a scalene triangle is also an altitude of the triangle. _____ 17. In a plane, if three points are each equidistant from the endpoints of a given
segment, then the three points are collinear. _____ 18. If two lines intersect to form two congruent adjacent angles, then the lines are
perpendicular. _____ 19. If the diagonals of a quadrilateral bisect each other, then it is a trapezoid. _____ 20. A rhombus is a parallelogram. _____ 21. In a quadrilateral, if only one diagonal bisects the opposite angles, then it is a kite. _____ 22. A diagonal of a parallelogram divides it into two congruent triangles. _____ 23. If both pairs of opposite angles in a quadrilateral are congruent, then it is a
rhombus. _____ 24. An equiangular triangle is isosceles. _____ 25. The number of diagonals in a polygon is equal to the number of vertices that it has. _____ 26. The exterior angle of a triangle is larger than any interior angle. _____ 27. If you double the lengths of the sides of a triangle, then you double the measures
