Jason uses the following steps to construct a perpendicular line through a point C on a line segment. Step 1: From point C, draw an arc intersecting the line segment in points A and B. Step 2: Using slightly more compass width, draw two arcs from point A, one above and the other below the line segment. Step 3: Using slightly more compass width, draw two arcs from point B, above and below the line segment. Step 4: Label the point of intersection of the arcs above the line segment as D and below the line as E. Step 5: Using a straightedge, join points D and E. Part A: Which is the first incorrect step? Part B: Using complete sentences, explain your answer for Part A. Part C: Explain why a compass works for the construction done by Jason. (10 points) Quadrilateral ABCD is located at A (-2, 2), B (-2, 4), C (2, 4), and D (2, 2). The quadrilateral is then transformed using the rule (x+2, y-3) to form the image A'B'C'D'. What are the new coordinates of A', B', C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments. (10 points) Triangle ABC is congruent to triangle DEF. In triangle ABC, side AB measures 6, side BC measures 5x-21, and side CA measures 5. In triangle DEF, side DE measures 6, side EF measures x-1, and side FD measures 5. What equation would help you to solve for the side length of BC and EF? Explain your reasoning using complete sentences. (10 points) Write an indirect proof to show that a rectangle has congruent diagonals. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted. (10 points) Rectangle ABCD is constructed with line EF drawn through its center. If the rectangle is dilated using a scale factor of 3 and a line is drawn through the center of the new dilated figure, what relationship will the new line have with line EF? Explain your reasoning using complete sentences. Matt is constructing two similar triangles for an art project. The drawing below shows Matt's plans, but there is an error in his drawing. What changes would he make to the dimensions to change the error? Explain your reasoning using complete sentences. (10 points) Prove the Pythagorean Theorem using similar triangles. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted. (10 A kite is a quadrilateral with two pairs of adjacent, congruent sides. The vertex angles are those angles in between the pairs of congruent sides. Prove the diagonal connecting these vertex angles is perpendicular to the diagonal connecting the nonvertex angles. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted. (10 points) Stephen is making a map of his neighborhood. He knows the following information: His home, the bus stop, and the grocery store are all on the same street. His home, the park, and his friend's house are on the same street. The angle between the park, the bus stop, and his home is congruent to the angle between his friend's house, the grocery store, and his home. What theorem can Stephen use to determine the remainin Pythagorean Theorem Triangle Proportionality Theorem Midsegment Theorem Side-Angle-Side Similarity Theorem Use ABC shown below to answer the question that follows: What statement is needed to prove that ABC is similar to DBA? (5 points) Segment BC is a hypotenu se. Angle B is congruent to itself. Segment BA is shorter than segment BC. Segment BC is intersecte d by segment AD. Look at the figure. What is the length, in units, of segment CD? (5 points) 5.50 12.2 5 8 14 Triangle MNO is dilated to form new triangle PQR. If angle O is congruent to angle R, what other information will prove that the two triangles are similar? (5 points) Side ON is congrue nt to side RQ. Angle N is congrue nt to angle Q. Side MN is congrue nt to side PQ. Angle M is congrue nt to angle Q. Quadrilateral ABCD in the figure below represents a scaled-down model of a walkway around a historic site. Quadrilateral EFGH represents the actual walkway. ABCD is similar to EFGH. What is the total length, in feet, of the actual walkway? (5 points) Tony photocopied the image of a design for a monorail track system. The figure below shows the design and its photocopy. The ratio of CD : BC is 2 : 3. The total length of track on the design is 58 meters. What is the length, in meters, of side GH on the photocopied image? (5 points) Read the statements shown below. If a closed figure has three line segments joined end to end, it is a triangle. If one angle of a triangle measures 90, it is a right triangle. Matt constructed a triangle with one angle measuring 90 in the geometry class. Based on the given statements, which is a valid argument? (5 points) It can be concluded that Matt drew a closed four-sided figure. It cannot be concluded that Matt drew a closed figure having three line segments joined end to end. It cannot be concluded that Matt drew a triangle with sum of all three angles measuring 180. It can be concluded that Matt drew a right triangle. In a quadrilateral ABCD, the diagonals bisect each other at point T. Based on the given conditions, which statement is presented first to show that triangle ATB is congruent to triangle CTD? (5 points) Diagonal AC is equal to side AB.Angle BTA is congruent to angle DTC.Side BC is equal to diagonal DB.Side BT is congruent to side CT