GEOMETRY ALL AROUND US!
BY SPENCER MILLER

? 1

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

? 2

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

? 3

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

? 4

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

? 5

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?

? 6

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.

? 7

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?

? 8

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

? 9

Use a construction to prove these lines parallel if possible.

? 10

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

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