幾何九式

Multiple Choice

Fill in the blanks to complete the geometric proof:

• A: ∠PQR = 38; B: Definition of Complementary Angles; C: Subtraction

  Property of Equality

• A: ∠PQR = 38; B: Definition of Supplementary Angles; C: Reflexive Property

• A: ∠PQR = 38; B: Definition of Vertical Angles; C: Transitive Property

• A: ∠PQR = 38; B: Definition of Complementary Angles; C: Substitution

Multiple Choice

What are the different methods to solve triangle problems related to length?

• S.S.S.

• A.A.S.

• R.H.S./H.L.

• S.A.S.

Multiple Choice

A manufacturer has daily production costs of
C = 20,000 − 40x + 0.055x²
where C is the total cost in dollars and x is the number of units produced. Graphically estimate the number of units that should be produced to yield a minimum cost.

• 58
• 127
• 364
• 652

Open Ended

If the two triangle shown are similar. What will the length of side EF?

Multiple Choice

如右圖，五邊形 ABCDE 中有一正三角形 ACD。若 AB=DE，BC=AE，∠E=115°，則∠BAE 的度數為何？

• 115

• 120

• 125

• 130

Fill in the Blanks

Multiple Choice

What is the ratio of BF to FG in triangle AFB and triangle AGB?

• 1:2

• 1:3

• 2:3

• 4:1

Multiple Choice

Fill in the reason for number 5. 

• Definition of congruent angles
• Angle Addition Postulate
• Substitution Property
• Transitive Property

Multiple Choice

In triangle ABC, if angle DFC is equal to 114 degrees, what is the measure of angle DFC?

• 114

• 123

• 132

• 147

Multiple Choice

In triangle ABC and triangle FGH, if points D and E are on AB and AC respectively, and F is on DE such that DE || FG and AB || AC, what is the area ratio of triangle ADE to triangle FGH?

• 2:1

• 3:2

• 5:2

• 9:4

Multiple Choice

How many friends are depicted on the front of the 1000 NT dollar bill?

• 4

• 5

• 6

• 7

Multiple Choice

What does 3V stand for in the context of this image?

• Vision

• Vitality

• Venture

• Victory

Multiple Choice

If AC = 6, AD = 8, AE = 5, AF = 9, and AB = 10, which of the following relationships is correct?

• AC + AD = AB

• AE + AF = AB

• AC + AD + AB

• AC + AE + AF = AB

Multiple Choice

Find the interval(s) of increase of the graph shown.

• (-6, -4)

• (-4, -2)

• (-2, 2)

• (2, 5)

• (5, 6)

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Multiple Choice

What are the coordinates of the circumcenter O of triangle ABC?

• (10, 21/2)

• (20, 21)

• (0, 0)

• (20, 0)

Multiple Choice

Which of the following is NOT an Ace card?

• Ace of spades

• Ace of hearts

• Ace of clubs

• Ace of diamonds

Multiple Choice

Which of the following is NOT a suit in a standard deck of cards?

• Hearts

• Diamonds

• Clubs

• Stars

Multiple Choice

If the polygon is regular, what is the measure of angle h?

• 360
• 540
• 72
• 108

Multiple Choice

求正八邊形邊長X

• X=2a

• X=a

• X=4a

• X=3a

Multiple Choice

What is the significance of the dashed lines in the square?

• They represent the diagonals of the square

• They indicate the area of the square

• They show the symmetry of the square

• They are just decorative lines

Multiple Choice

What is the significance of the dashed lines in triangle ABC?

• They represent the angle bisectors

• They indicate the midpoints of the sides

• They show the height of the triangle

• They are used to divide the triangle into two equal areas

Multiple Choice

What is the angle bisector of angle ABC?

• A line that divides the angle into two equal parts

• A line that is perpendicular to the opposite side

• A line that connects the vertex to the opposite side

• A line that is parallel to the opposite side