In the diagram of shown below, use a compass and straightedge to construct the median to . [Leave all construction marks.]
Construct the median to using a compass and straightedge.
Answer all 7 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil.
Triangle is the image of triangle after a dilation with a scale factor of and centered at point . Is triangle congruent to triangle ? Explain your answer.
Determine and state the area of triangle , whose vertices have coordinates , and .
A support wire reaches from the top of a pole to a clamp on the ground. The pole is perpendicular to the level ground and the clamp is 10 feet from the base of the pole. The support wire makes a angle with the ground. Find the length of the support wire to the nearest foot.
In the diagram below, circle has a radius of 10 .
If , find the area of shaded sector , in terms of .
On the set of axes below, .
Describe a sequence of rigid motions that maps onto .
In right triangle , altitude is drawn to hypotenuse , and .
Determine and state, to the nearest tenth, the length of .
Given circle with radius , use a compass and straightedge to construct an equilateral triangle inscribed in circle . [Leave all construction marks.]
Using a compass and straightedge, construct the median to side in below. [Leave all construction marks.]
Construct the median to side .
Triangle is shown below. Using a compass and straightedge, on the line below, construct and label , such that . [Leave all construction marks.] Based on your construction, state the theorem that justifies why is congruent to .
Construct and label such that it is congruent to .
State the theorem that justifies the congruence of and .
The regular polygon below is rotated about its center. Which angle of rotation will carry the figure onto itself?
A regular decagon is rotated degrees about its center, carrying the decagon onto itself. The value of could be
Use a compass and straightedge to construct a line parallel to through point , shown below. [Leave all construction marks.]
Use a compass and straightedge to construct a line parallel to through point . [Leave all construction marks.]
Which quadrilateral has diagonals that are always perpendicular?
Given: Trapezoid JKLM with Using a compass and straightedge, construct the altitude from vertex to . [Leave all construction marks.]
Construct the altitude from vertex to using a compass and straightedge.
Triangle is shown below. Using a compass and straightedge, construct the dilation of centered at with a scale factor of 2. [Leave all construction marks.]
Is the image of similar to the original triangle? Explain why.