Sharon Briggs of Montgomery Village needed two playoff holes to defeat co-medalist Lorraine Elder of Army Navy and Florida State in their quarterfinal match yesterday in the Women's District Golf Association championship at International.

Briggs today will play Michelle Mackall of Montgomery County Club, who defeated Kathy Malpass of Montgomery Village, 5 and 3.

In the other quarterfinals, co-medalist Brenda Seymour of Hidden Creek defeated Fran Schultz of Army Navy, 4 and 3, and in a match with only one birdie, Lois Ledbetter of Lakewood (Ala.) beat seniors medalist Nancy Hollenbeck, 2 and 1.

Briggs three-putted on the ninth green for a one-stroke lead after nine holes. Elder hit her second shot on the 14th into the trap and Briggs capitalized to go 2 up. Though her backswing was restricted by a tree on her second shot, Elder made par on the 15th to tie the hole.

On the par-3 17th hole, Elder hit her tee shot about seven feet from the cup while Briggs teed off into the rough. Briggs then missed her putt for par.

On the 18th, Elder, who shot 74 in Monday's qualifying round, sank a 12-foot putt to force the playoff. On the first sudden-death hole, a par-5, each reached the green in three and was left with seven-foot birdie putts, Briggs' uphill and Elder's downhill. Each made par.

On the second playoff hole, a par-4, Elder put her second shot into the trap. Her third shot landed 35 feet from the cup. Meanwhile, Briggs birdied the hole and won the match.

Ledbetter was one down after nine but won the 10th, 13th, 14th and 17th holes without making a birdie to take her quarterfinal match.