Answer:
1.a.SAS axiom
b. ASA axiom
Explanation:
There are five basic conditions for triangles to be congruent:
- SSS:
If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent. - SAS:
If two sides and the included angle of one triangle are equal to the two sides and the included angle of another triangle, then the two triangles are congruent. - ASA:
If two angles and the included side of one triangle are equal to the two angles and the included side of another triangle, then the two triangles are congruent. - AAS:
If two angles and the non-included side of one triangle are equal to the two angles and the non-included side of another triangle, then the two triangles are congruent. - RHS:
If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
For Question:
1.
a. InΔABC and ΔBCD
AB=CD opposite sides of the parallel line are equal Side
∡BAC=∡BDA Given Angle
BC=BC Same side Side
It fulfills the condition of the SAS axiom,
InΔABC ≅ ΔBCD by SAS axiom
b. InΔABC and ΔCDE
∡ACB=∡DCE Vertically opposite angle Angle
BC=CD given Side
∡ABC=∡CDE right angle Angle
It fulfills the condition of the ASA axiom,
InΔABC ≅ ΔCDE by ASA axiom It may be R.H.S. axiom too.