### GEOMETRY ALL AROUND US!

BY SPENCER MILLER

## ? 1

What postulate would you use to find that these two triangles are similar?

Line C is parallel to line B, when angle Z measures 164, find the measure of angle X.

Plane E is parallel to the building, line A lies on top of plane E, what is line A to plane E?

If line XZ are parallel to line AD, what two triangles are similar?

All of the red lines are parallel to each other, and the gray lines are parallel to each other, and the measure of segment X equals 15, then what is the measure of Y is congruent to segment X, then are the 3 parallel lines equal distance apart from each other?

All red lines are parallel to each other, and the measure of angle 1 is 102, then find the measurements for angles 2, 3, 4, 5, 6, 7, and 8.

The red lines represent a plane, and the dark gray lines represent separate lines that are parallel to the red line plane, what are these gray lines in comparison to the red?

Prove these two triangles congruent, if not congruent, then say not congruent and why.

Use a construction to prove these lines parallel if possible.

Taxiway B is perpendicular to Runway A, what type of lines are the two remaining Runways? The other Runways are Dark Grey lines.

ANSWERS!

? 1: SAS ~ because there is a side, angle, and side that are similar, and in that order.

? 2: Angle X = 164 because angle X is a vertical angle

? 3: Coplanar because of the line lies on the plane

? 4: Triangle XZB ~ Triangle DAC because angle A is congruent to angle Z, and angles C and B are vertical angles

? 5: Measure of segment Y = 15 and the red lines that X and Y fall between are equal distance apart from each other

? 6: (< means angle) < 2= 78, <3=78, <4=102, <5=102, <6=78, <7=78, <8=102 because of vertical, alternate, corresponding, and consecutive angles

? 7: non coplanar because they never intersect or touch

? 8: not congruent, not enough information

? 9: Parallel lines construction because this construction proves lines parallel or not parallel

? 10: Oblique Lines because the intersect, but do not form a right (90 degree) angle