Question

a
if ko = on and mo = ol, then δkol ≅ δnom.
b
if n is a midpoint of segment km and kl = ml, then δkln ≅ δmln.
c
if kl || mn and kl = mn, then δkol ≅ δnom.
match postulates with the figures

1. asa postulate
2. sss postulate
3. sas postulate

Explanation:

Step1: Analyze Figure A

Given $KO=ON$, $MO=OL$, and $\angle KOL = \angle NOM$ (vertical angles). This satisfies the Side-Angle-Side (SAS) condition: two sides and the included angle of $\Delta KOL$ equal to those of $\Delta NOM$.

Step2: Analyze Figure B

Given $N$ is midpoint of $KM$ so $KN=MN$, $KL=ML$, and $LN=LN$ (common side). This satisfies the Side-Side-Side (SSS) condition: all three sides of $\Delta KLN$ equal to those of $\Delta MLN$.

Step3: Analyze Figure C

Given $KL \parallel MN$ so $\angle LKO = \angle MNO$ and $\angle KLO = \angle NMO$ (alternate interior angles), plus $KL=MN$. This satisfies the Angle-Side-Angle (ASA) condition: two angles and the included side of $\Delta KOL$ equal to those of $\Delta NOM$.

Answer:

1. ASA postulate - Figure C
2. SSS postulate - Figure B
3. SAS postulate - Figure A