Is triangle ADB congruent to triangle CDB by SAS, AAS, ASA, SSS, or HL? If segment AB is congruent to segment CB and segment BD bisects segment AC. http://media.cheggcdn.com/media/022/022a99f9-aed4-4707-a9da-90b40929aab9/phpg9oyuq.png
- print Print
- list Cite
Expert Answers
Eric Bizzell
| Certified Educator
briefcaseTeacher (K-12)
calendarEducator since 2011
write3,148 answers
starTop subjects are Math, Science, and Business
We are given `Delta ABC` with `bar(AB) cong bar(CB)` and `bar(BD)` bisects `bar(AC)` at `D` .
(1) Since AB=CB we know that angles A and C are congruent from the isosceles triangle theorem. Also since `bar(AC)` is bisected at D, we have AD=CD so the `Delta ADB cong Delta CDB` by SAS
(2) BD=BD by the reflexive property. Since AD=CD you could use SSS.
(3) If you know that the median drawn from the vertex angle of an isosceles triangle is also the angle bisector of the vertex angle, the altitude drawn from the vertex angle, and the perpendicular bisector of the base then you could use any of AAS,ASA, or H-L.
Related Questions
- Can the two triangles be proved congruent? If so, by which method: sss, sas, asa, aas, or hl....
- 1 Educator Answer
- Given https://pbs.twimg.com/media/BXJYmRuIgAAT6p1.jpg:large,: DB bisects Angle ADC and BD bisects...
- 1 Educator Answer
- ABCD is a rhombus. M and N are points on BD such that DN = MB. Prove that Triangle DNC is...
- 1 Educator Answer
- Congruent triangles SSS and SAS proofs. Write a 2 column for each of the following problem. No...
- 1 Educator Answer
- In order to prove that triangle ABE is congruent to triangle CBD by ASA we would need to show that
- 1 Educator Answer