# Geometry All Around Us!

### Question 1:

The two lines indicated are parallel. Lines have been extended for easier viewing. What is the relationship between angles 1 & 3? What about angles 2 & 4? Also, what would be the values of x & y?

### Question 2:

Are these two street signs perpendicular, parallel, skew, or something else?

### Question 3:

Do all of these shapes tessellate? If so, what shapes do they make?

Since we know all of the angles of this hexagon are equal from the above annotated image, what is the measure of x? (hint: it is an interior angle)

### Question 4:

In this picture, there are four obvious triangles. There are two sets of two different types of triangles. Name these types and then find the measure of x. (Figure not drawn to scale.)

### Question 5:

Line RS is a bisector of angle QRT. What construction of geometry does this demonstrate an example of? Also, what type of quadraleteral is the entire shape?

### Question 6:

Using the above picture, identify which postulate of congruent triangles you can use to prove these two triangles congruent.

### Question 7:

Using the above picture, find out how many diagonals can be drawn from one vertex. Then, find the measure of ALL of the interior angles.

### Question 8:

What is the measure of each exterior angle on this stop sign?

### Question 9:

Using the above picture, and your knowledge of the Triangle Inequality Theorem, can you prove that the shape indicated is an existing triangle? Why or why not?

### Question 10:

The two triangles above in this bridge are right triangles. To prove these two triangles are congruent, which postulate(s) should you use?

(Hint: There is more than one answer)

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Question 1.) The relationship between angles 1 & 3 is that they are alternate interior angles. Angles 2 & 4 also are alternate interior angles. We do not know the values of x & y because there is not enough information. We just know that x=y, because they are alternate interior angles.

Question 2.) The two signs are perpendicular to one another.

Question 3.) They are hexagons and yes, they do tessellate; x= 120 degrees

Question 4.) There are two right triangles and two isosceles triangles in this picture. X = 36 degrees.

Question 5.) This is an example of an angle bisector. If we go back to what we learned about angle bisectors, we know that bisection is when something (usually a line) divides an angle into two congruent parts. Finally, the shape is a rhombus.

Question 6.) You can use the postulate of Side-Angle-Side to prove these two triangles congruent. We know this because of the hash marks each triangle has.

Question 7.) You can draw five diagonals from one vertex of this octagon. The measure of all of the interior angles is 1080 degrees. Use the interior angle formula for this problem. The formula is 180(n-2).

Question 8.) Since we know that the measure of all exterior angles in a polygon is 360 degrees, divide 360 by 8, since we are dealing with an octagon, and you get 45 degrees for each exterior angle.

Question 9.) Yes, the shape indicated is a triangle. We know this because as long as any two sides are longer than any third side, a triangle exists. (The Triangle Inequality Theorem)

Question 10.) You should use the triangle postulate of HL, or hypotenuse-leg. This is because whenever there are two right triangles involved (and it specifically states that they are right triangles) that have congruent legs to each other and congruent hypotenuses, then we know right away to use the postulate HL. However, another answer you could have chosen would be the postulate of SAS (Side-Angle-Side). We know this because there is a side and then an angle, followed by a final side. Either of the two postulates stated above could have been chosen.