Name:

**Geometry Part 1 Midterm**

**Directions:** Please make sure to justify **all** answers. This includes showing work with necessary or providing adequate explanation.

1. Write a paragraph proof.

Given: ∠*T* and ∠*V* are right angles.

Prove: ∆*TUW* ∆*VWU*

2. Sled kites rely on wind pressure to retain the shape of the sail. Each consists of a single square and two triangular pieces. Kyle has made a model of a Sled kite as shown below. Show that the angles and are congruent.

**(JUSTIFY)**

3. A ray of light is reflected when it hits a mirror. The angle at which the light strikes the mirror is the *angle of incidence*, *i*. The angle at which the light is reflected is the *angle of reflection*, *r*. The angle of incidence and the angle of reflection are congruent. In the diagram below, if , what is the angle of reflection and

**(JUSTIFY)**

4. Samantha has cut a pastry into four parts. Suppose and *T* is the midpoint of *PR*. Determine whether **Justify your answer.**

5. A pathway divides a rectangular garden into two parts as shown. Find the measure of

**(JUSTIFY)**

6. Andy was playing a memory game with his sister. He turned over a tile to reveal a picture of the sun at the coordinates (5, 4). He looked under a tile that was 3 units to the left and 2 units down but revealed a picture of a tree. His sister knew that the other sun was 1 unit to the left and 1 unit up from the tree. What are the coordinates of the second sun?

**(JUSTIFY)**

7. Carpenters use parallel wall studs to build support for walls. A carpenter has built two wall studs given by *HG* and *CD* in the figure below. Find the measure of so that the two wall studs are parallel.

**(JUSTIFY)**

8. Richard ordered a coffee table that was a regular pentagon. Find the measure of an exterior angle of the table.

**(JUSTIFY)**

*Use trapezoid ABCD to find each measure.*

9. Let be the median of *LMBA*. Find , , and .

**(JUSTIFY)**

10. In a museum, Nick is looking at a famous painting through a mirror at an angle of Find the angle the painting makes with the mirror. Also find and

**(JUSTIFY)**

11. If a bike tire has 16 spokes spaced evenly apart, name its **angles** of rotation.

**(JUSTIFY)**

12. Richard wants to buy a LCD flat panel monitor measuring 14 inches by 16 inches. What is the measure of the diagonal of the monitor?

**(JUSTIFY)**

13. Samantha’s rectangular gift is 10 inches. by 12 inches and is framed with a ribbon. She wants to use the same length of ribbon to frame a circular clock. What is the maximum radius of the circular clock? Round to the nearest whole number.

**(JUSTIFY)**

*Write a two-column proof.*

14. **Given:** is the perpendicular bisector of

**Prove:**

15. Write a flow proof for the problem. **Given:** **Prove:**

*Write a two-column proof.*

16. Find the coordinates of the orthocenter of Δ*YAB* that has vertices at *Y*(3, –2), *A*(3, 5), and *B*(9, 1). **(JUSTIFY)**

17. For isosceles trapezoid *ABCD*, find the length of the median and .**(JUSTIFY)**

18. Write a two-column proof.

Given:

and are rt.

Prove: ∆*ABC* *∆ADC*

19. A salesperson travels from city A to city B and then to city C. From city C, the salesperson travels directly back to city A as shown in the diagram below. Write the lengths of the legs of the trip in order from least to greatest.

**(JUSTIFY)**

20. A construction manager moved a shed to the back corner of a lot. Because there were so many trees in the way, the construction manager had to move it 6 units up, 2 units to the left, 2 units down, and 3 units to the left. The vertices are now (5, 5), (0, 5), (5, 3), and (0, 3). What were the original vertices of the shed?

**(JUSTIFY)**