Assignment: 4.6 on p. 231: 1-4
Questions all apply to this figure
1. Are angles 1 and 2 congruent in the figure?
2. Are angles 3 and 4 congruent in the figure?
3. What else would you need to know in order to prove triangle ABD and triangle CDB are congruent?
1. Yes, angles 1 and 2 are congruent because they are alternate interior angles formed by parallel lines CB and AD and the transversal BD.
2. Cannot be determined. Since we do not know if CD and AB are parallel, we cannot say whether or not angles 3 and 4 are congruent. To avoid doing assuming we can eyeball parallel lines you could imagine the shape with AD still parallel to segment BC but if BC and AD are different lengths angle 3 and 4 can have different measurements.
3. Many possible answers. Here are a few
- If we knew that BC = AD we could prove the triangles congruent by SAS.
- If we knew that angle 3 and 4 were congruent, we could use ASA
- If we knew that angle C and angle A were congruent, we could use AAS.