Checkpoint: earning the name

A quadrilateral has one pair of opposite sides equal. Nothing is known about the other pair. What does that force?

• It is a parallelogram, since one pair of sides matches
• Nothing about the name, since one pair proves nothing
• It must be a trapezium, since one pair of sides is equal

In quadrilateral ABCD, diagonal AC lands triangle ABC exactly on triangle CDA. Which step forces AB parallel to DC?

• The two triangles share the side AC
• AB and DC look parallel once the diagonal is drawn
• Angles BAC and DCA are an equal alternate pair

A quadrilateral has AB = DC = 6 and BC = AD = 4. Which congruence lands triangles ABC and CDA?

• SAS, since a diagonal makes an angle
• SSS, since all three pairs of sides match
• None, since four lengths prove nothing

The diagonals of ABCD cross at O. OA = OC and OB = OD. Which fact lands triangles AOB and COD?

• Angle A equals angle C
• The vertically opposite angles at O are equal
• The diagonals are equal in length, as in a rectangle

In triangle ABC, D is on AB and E is on AC. Both are midpoints. What does the midpoint theorem say about DE?

• DE equals BC, and runs parallel to it
• DE equals half of BC, and runs parallel to BC
• DE equals half of AB, and runs parallel to AB