Geometry · Unit 2
Read a figure, then decide whether each statement is true or false.
Jump to section:
Collinear and coplanar
Collinear points lie on the same line.
Coplanar points lie on the same plane.
Any three points are coplanar. Four points are coplanar only when one plane holds all four.
Intersection
Two lines intersect in one point, or they do not intersect.
Name the point you see on both lines.
Rays
A ray has one endpoint and goes on in one direction.
The same ray: same endpoint, same direction.
Opposite rays: same endpoint, opposite directions, together a line.
Vertical angles and angle addition
Vertical angles are opposite each other at a crossing. They are congruent.
If a ray is in the interior of an angle, the two pieces add to the whole angle.
Points, lines, and a plane.
Not drawn to scale.
1. Points A, B, and C are collinear.
2. Points A, B, and D are collinear.
3. Line AC and line DE intersect at B.
4. Points A, D, F, and B are coplanar.
5. Points A, D, F, and G are coplanar.
1. True. They lie on one line.
2. False. A and B are on one line. D is on the other line.
3. True. The two lines cross at B.
4. True. All four points are on plane P.
5. False. A, D, and F are not on one line, so they determine plane P. G is not on that plane.
Answer: 1 true; 2 false; 3 true; 4 true; 5 false
Not drawn to scale.
1. Points J, K, and L are collinear.
2. Points J, K, and M are collinear.
3. Line JL and line MN intersect at K.
4. Points J, M, Q, and K are coplanar.
5. Points J, M, Q, and R are coplanar.
1. True. They lie on one line.
2. False. J and K are on one line. M is on the other line.
3. True. The two lines cross at K.
4. True. All four points are on plane W.
5. False. J, M, and Q are not on one line, so they determine plane W. R is not on that plane.
Answer: 1 true; 2 false; 3 true; 4 true; 5 false
Not drawn to scale.
1. Points P, Q, and R are collinear.
2. Points P, Q, and S are collinear.
3. Line PR and line ST intersect at Q.
4. Points P, S, U, and Q are coplanar.
5. Points P, S, U, and V are coplanar.
1. True. They lie on one line.
2. False. P and Q are on one line. S is on the other line.
3. True. The two lines cross at Q.
4. True. All four points are on plane M.
5. False. P, S, and U are not on one line, so they determine plane M. V is not on that plane.
Answer: 1 true; 2 false; 3 true; 4 true; 5 false
Not drawn to scale.
1. Points A, C, and E are collinear.
2. Points A, C, and B are collinear.
3. Line AE and line BD intersect at C.
4. Points A, B, F, and C are coplanar.
5. Points A, B, F, and G are coplanar.
1. True. They lie on one line.
2. False. A and C are on one line. B is on the other line.
3. True. The two lines cross at C.
4. True. All four points are on plane N.
5. False. A, B, and F are not on one line, so they determine plane N. G is not on that plane.
Answer: 1 true; 2 false; 3 true; 4 true; 5 false
Not drawn to scale.
1. Points W, X, and Y are collinear.
2. Points W, X, and U are collinear.
3. Line WY and line UV intersect at X.
4. Points W, U, Z, and X are coplanar.
5. Points W, U, Z, and T are coplanar.
1. True. They lie on one line.
2. False. W and X are on one line. U is on the other line.
3. True. The two lines cross at X.
4. True. All four points are on plane R.
5. False. W, U, and Z are not on one line, so they determine plane R. T is not on that plane.
Answer: 1 true; 2 false; 3 true; 4 true; 5 false
Not drawn to scale.
1. Points B, D, and F are collinear.
2. Points B, D, and A are collinear.
3. Line BF and line AC intersect at D.
4. Points B, A, E, and D are coplanar.
5. Points B, A, E, and G are coplanar.
1. True. They lie on one line.
2. False. B and D are on one line. A is on the other line.
3. True. The two lines cross at D.
4. True. All four points are on plane S.
5. False. B, A, and E are not on one line, so they determine plane S. G is not on that plane.
Answer: 1 true; 2 false; 3 true; 4 true; 5 false
Same ray, or opposite rays.
Not drawn to scale.
1. Ray BA and ray BD are the same ray.
2. Ray BA and ray BC are opposite rays.
3. Ray AB and ray BA are the same ray.
4. Ray AB and ray AC are the same ray.
5. E is on the line.
1. True. Both start at B and go through A and D.
2. True. A–B–C is a line, and B is between A and C.
3. False. They start at different endpoints.
4. True. Both start at A and go through B and C.
5. False. E is off the line.
Answer: 1 true; 2 true; 3 false; 4 true; 5 false
Not drawn to scale.
1. Ray RQ and ray RP are the same ray.
2. Ray QR and ray QS are the same ray.
3. Ray RQ and ray RS are the same ray.
4. Ray SR and ray SQ are the same ray.
5. Q, R, and T are collinear.
1. True. Both start at R and go through Q and P.
2. True. Both start at Q and go through R and S.
3. False. They start at R and go opposite ways.
4. True. Both start at S and go through R and Q.
5. False. T is off the line.
Answer: 1 true; 2 true; 3 false; 4 true; 5 false
Not drawn to scale.
1. Ray ML and ray MK are the same ray.
2. Ray LM and ray LN are the same ray.
3. Ray KL and ray KN are the same ray.
4. Ray NM and ray NK are opposite rays.
5. H, L, and M are collinear.
1. True. Both start at M and go through L and K.
2. True. Both start at L and go through M and N.
3. True. Both start at K and pass through L, M, and N.
4. False. They are the same ray. Both start at N and go through M and K.
5. False. H is off the line.
Answer: 1 true; 2 true; 3 true; 4 false; 5 false
Not drawn to scale.
1. Ray EC and ray EA are the same ray.
2. Ray CE and ray CG are opposite rays.
3. Ray EA and ray EG are opposite rays.
4. Ray AC and ray AG are the same ray.
5. A, E, and B are collinear.
1. True. Both start at E and go through C and A.
2. False. They are the same ray.
3. True. A–E–G is a line, with E between A and G.
4. True. Both start at A and go through C, E, and G.
5. False. B is off the line.
Answer: 1 true; 2 false; 3 true; 4 true; 5 false
Not drawn to scale.
1. Ray HG and ray HF are the same ray.
2. Ray GH and ray GJ are the same ray.
3. Ray FG and ray FJ are the same ray.
4. Ray JH and ray JF are opposite rays.
5. G, H, and K are collinear.
1. True. Both start at H and go through G and F.
2. True. Both start at G and go through H and J.
3. True. Both start at F and go through G, H, and J.
4. False. Same endpoint, same direction.
5. False. K is off the line.
Answer: 1 true; 2 true; 3 true; 4 false; 5 false
Not drawn to scale.
1. Ray PN and ray PM are the same ray.
2. Ray NP and ray NQ are the same ray.
3. Ray PN and ray PQ are opposite rays.
4. Ray QN and ray QM are the same ray.
5. N, P, and R are collinear.
1. True. Both start at P and go through N and M.
2. True. Both start at N and go through P and Q.
3. True. M–N–P–Q is a line, and the rays leave P in opposite directions.
4. True. Both start at Q and go through P, N, and M.
5. False. R is off the line.
Answer: 1 true; 2 true; 3 true; 4 true; 5 false
Vertical angles and angle addition, from one figure.
Not drawn to scale.
1. ∠AEB ≅ ∠CED.
2. ∠AEB ≅ ∠AED.
3. m∠AEF + m∠FEB = m∠AEB.
4. m∠AEF + m∠FEB = m∠AED.
5. Ray EA and ray EC are opposite rays.
1. True. They are vertical angles.
2. False. They are a linear pair. They add to 180°. They are congruent only when each is 90°.
3. True. Ray EF is between the sides of ∠AEB, so the two pieces add to the whole angle.
4. False. The left side is ∠AEB. The right side is the linear pair next to it, not the same angle.
5. True. A, E, and C are collinear, with E between A and C.
Answer: 1 true; 2 false; 3 true; 4 false; 5 true
Not drawn to scale.
1. ∠POQ ≅ ∠ROS.
2. ∠POQ ≅ ∠POS.
3. m∠POT + m∠TOQ = m∠POQ.
4. m∠POT + m∠TOQ = m∠POS.
5. Ray OP and ray OR are opposite rays.
1. True. They are vertical angles.
2. False. They are a linear pair. They add to 180°. They are congruent only when each is 90°.
3. True. Ray OT is between the sides of ∠POQ, so the two pieces add to the whole angle.
4. False. The left side is ∠POQ. The right side is the linear pair next to it, not the same angle.
5. True. P, O, and R are collinear, with O between P and R.
Answer: 1 true; 2 false; 3 true; 4 false; 5 true
Not drawn to scale.
1. ∠AMB ≅ ∠CMD.
2. ∠AMB ≅ ∠AMD.
3. m∠AME + m∠EMB = m∠AMB.
4. m∠AME + m∠EMB = m∠AMD.
5. Ray MA and ray MC are opposite rays.
1. True. They are vertical angles.
2. False. They are a linear pair. They add to 180°. They are congruent only when each is 90°.
3. True. Ray ME is between the sides of ∠AMB, so the two pieces add to the whole angle.
4. False. The left side is ∠AMB. The right side is the linear pair next to it, not the same angle.
5. True. A, M, and C are collinear, with M between A and C.
Answer: 1 true; 2 false; 3 true; 4 false; 5 true
Not drawn to scale.
1. ∠WQX ≅ ∠YQZ.
2. ∠WQX ≅ ∠WQZ.
3. m∠WQV + m∠VQX = m∠WQX.
4. m∠WQV + m∠VQX = m∠WQZ.
5. Ray QW and ray QY are opposite rays.
1. True. They are vertical angles.
2. False. They are a linear pair. They add to 180°. They are congruent only when each is 90°.
3. True. Ray QV is between the sides of ∠WQX, so the two pieces add to the whole angle.
4. False. The left side is ∠WQX. The right side is the linear pair next to it, not the same angle.
5. True. W, Q, and Y are collinear, with Q between W and Y.
Answer: 1 true; 2 false; 3 true; 4 false; 5 true
Not drawn to scale.
1. ∠AKB ≅ ∠CKD.
2. ∠AKB ≅ ∠AKD.
3. m∠AKE + m∠EKB = m∠AKB.
4. m∠AKE + m∠EKB = m∠AKD.
5. Ray KA and ray KC are opposite rays.
1. True. They are vertical angles.
2. False. They are a linear pair. They add to 180°. They are congruent only when each is 90°.
3. True. Ray KE is between the sides of ∠AKB, so the two pieces add to the whole angle.
4. False. The left side is ∠AKB. The right side is the linear pair next to it, not the same angle.
5. True. A, K, and C are collinear, with K between A and C.
Answer: 1 true; 2 false; 3 true; 4 false; 5 true
Not drawn to scale.
1. ∠RTS ≅ ∠UTV.
2. ∠RTS ≅ ∠RTV.
3. m∠RTW + m∠WTS = m∠RTS.
4. m∠RTW + m∠WTS = m∠RTV.
5. Ray TR and ray TU are opposite rays.
1. True. They are vertical angles.
2. False. They are a linear pair. They add to 180°. They are congruent only when each is 90°.
3. True. Ray TW is between the sides of ∠RTS, so the two pieces add to the whole angle.
4. False. The left side is ∠RTS. The right side is the linear pair next to it, not the same angle.
5. True. R, T, and U are collinear, with T between R and U.
Answer: 1 true; 2 false; 3 true; 4 false; 5 true
Need help reading a figure of points, lines, and planes?
Book a Session with Amy