In the figure below, the following is true: angleABD congruent to angleCDB and angleDBC congruent to angleBDA. How can you justify that triangleABD congruent to triangleCDB?
Two triangles A B D and C D B are shown with a common segment B D. Segment A B appears to be parallel to D C. A D appears to be parallel to B C.
(1 point)
Responses
SAS
SAS
SSS
SSS
ASA
ASA
CPCTC
To justify that triangle ABD is congruent to triangle CDB, we can use the ASA (Angle-Side-Angle) congruence postulate.
1. We are given that angle ABD is congruent to angle CDB (given: angleABD congruent to angleCDB).
2. We are also given that angle BDA is congruent to angle DBC (given: angleDBC congruent to angleBDA).
3. Segment BD is congruent to itself (reflexive property).
Using the ASA congruence postulate, we have two pairs of congruent angles (angle-angle) and a pair of congruent corresponding sides (side-side). Therefore, triangle ABD is congruent to triangle CDB.
To justify that triangle ABD is congruent to triangle CDB, we can use the SAS (Side-Angle-Side) congruence criterion.
SAS states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In this case, we have:
1) angle ABD congruent to angle CDB (given)
2) segment BD common to both triangles
3) angle CDB congruent to angle BDA (given)
Therefore, we have two pairs of congruent angles (ABD ≅ CDB and CDB ≅ BDA) and one pair of congruent sides (BD).
Applying the SAS criterion, we can conclude that triangle ABD is congruent to triangle CDB.
To justify that triangle ABD is congruent to triangle CDB, we can use the SAS (Side-Angle-Side) congruence criterion.
SAS states that if two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the triangles are congruent.
In this case, we are given that angle ABD is congruent to angle CDB and angle DBC is congruent to angle BDA. Additionally, we can see that segment BD is shared by both triangles.
To apply the SAS criterion, we need to show that the sides AD and BC are congruent. We can do this by using the information given: segment AB appears to be parallel to segment DC, and segment AD appears to be parallel to segment BC.
By the properties of parallel lines, we can conclude that the corresponding angles ABD and CDB, as well as angles DBC and BDA, are congruent.
Therefore, by the SAS criterion, we can justify that triangle ABD is congruent to triangle CDB.