Track quiz

Ten ideas, eleven checks. The table sits first, so there is somewhere to look back.

Lines and angles — ten moves, and what each one gives you
Idea	How it goes
Cross or never	Two lines meet once, or never. There is no third case.
Parallel	Never meeting, same gap everywhere, measured square across.
Opposite angles	Angles facing across a crossing are equal, however the page turns.
On a line	Angles on a line add to 180°. All round a point, 360°.
The transversal	One line across two makes eight angles. Three pair names: corresponding, alternate, co-interior.
The condition	Those three pair facts hold only on parallel lines. A tilt breaks them by exactly its own size.
Chasing an angle	Move one named fact at a time. Say which fact each step used.
Perpendicular	Two lines that cross at a right angle are perpendicular. If one of the four angles is 90°, all four are. A small square marks the corner.
Square to a third line	On a flat page, two lines perpendicular to one line are parallel. Mark parallel lines with arrows. Mark a right angle with a small square.
A bend between parallels	A path bends at O between two parallel lines. Its two ends lie on the same side of O. At each end, mark the angle that opens towards O. Draw a parallel through O. Alternate angles are equal. So the bend is the sum of the two marked angles.

Two different straight lines are drawn on one flat page. How many points can they share?

Any number, depending on how long you draw them
One, or none at all
Two, at most

Two lines run across a page without meeting anywhere on it. What does that prove?

They are parallel, because they do not meet
They are not parallel, because the page is too small to tell
Nothing on its own. They may meet far past the edge of the page

Two lines are drawn on a page. Their gap is measured square across at each edge. It reads 15 steps at one edge. It reads 13 steps at the other. Parallel?

No — parallel lines hold the same gap everywhere
Yes, because 15 and 13 are close
There is no way to tell without extending the page

Two lines cross. One of the four angles is 72°. What is the angle facing it across the crossing point?

108°
72°
18°

Three angles sit side by side on a straight line. Two of them are 40° and 65°. What is the third?

105°, because that is what the first two make
255°, because a full turn is 360°
75°

A transversal cuts two parallel lines. One of the eight angles is 65°. What is its co-interior partner?

115°
65°, because named pairs are equal
25°, because they make a right angle together

A transversal cuts two lines. A corresponding pair is exactly 65° and 64°. What can you say?

Nothing — 1° is measuring error, so treat them as equal
The two lines are not parallel, and they are 1° out
The pair was named wrongly, since corresponding angles are always equal

A 52° angle sits at the upper crossing of two parallel lines. Walk along the straight line. Then go to the matching corner at the lower crossing. What do you reach?

52°, because both steps leave the number alone
232°, because the two steps add up
128°

Two lines cross. One of the four angles is 90°. What are the other three?

All three are 90°
90°, 270° and 90°
It depends on how long the lines are

A set square slides along a ruler. Two lines are drawn along its square edge. What do you know about them?

They are perpendicular to each other
They are parallel, because both are square to the ruler
They meet at the ruler

A path bends between two parallel lines. Its ends lie on the same side of the bend. The marked end angles are 36° and 58°. How wide is the bend?

22°
86°
94°

Chapter 5 of Part I is Parallel and Intersecting Lines. Open it and check each fact against its pictures.

Next: Number Play — digit sums and tricks that always work. Also, proving that one really does.

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