A 17-year-old senior was fatally shot yesterday inside a building of Forestville High School and, in an unrelated incident, a basketball player at the District's Coolidge High School was shot and killed as he was leaving his home for classes, police reported.

The deaths stunned the two high schools, where officials described the two youths as good, hard-working, polite students. Prince George's County school officials said they did not know of another fatal shooting that occurred inside a school building.

The victims were identified as Dwayne Satterwhite of 700 Pritchard La., Largo, and Andre Jackson, 18, of 44 Q St. NE.

No other persons were injured in either incident.

Prince George's County police said last night that they were seeking three youths seen running from where Satterwhite was shot.

A D.C. police source said last night that officers are looking for a man who may have been an acquaintance of Jackson. The source said a witness told police that he had previously seen the man in Jackson's home. No arrests had been made in either shooting late last night.

Police said Satterwhite was shot during school hours yesterday, minutes after talking with a teacher and another student.

Witnesses told police that shortly before 2 p.m. they heard gunfire and soon afterward saw Satterwhite stagger out of a school annex building and across a parking lot toward the main school building. He collapsed near the front door of the building, witnesses told police.

Satterwhite, who had been shot once in the head, was pronounced dead a short time later at Prince George's General Hospital, police said.

As police investigators combed a small wooded area and shrubbery near the annex for possible evidence, students and teachers were kept inside the building.

Students were allowed to leave the building at the end of classes, but county school buses were directed to the rear of the complex to keep the crime scene secure.

Maj. David Ross, head of the county police criminal investigation division, said it was not known if the three persons seen running from the scene were students or former students at the school, at 7001 Beltz Dr., Forestville.

Ross said police have some information about the identity of one of the youths. He said they do not have a motive for the shooting.

Forestville Principal Paul R. Lewis and other school officials referred all questions about the shooting to police. Teachers who talked about the incident and Satterwhite asked that their names not be published.

A social studies teacher said Satterwhite had talked with him about a half hour before the shooting and asked about getting a job as a teacher's aide. The teacher said Satterwhite later talked with another student about joining the U.S. Marines after graduation in the spring.

"He's the type of kid you just know would have amounted to something," the teacher said. "He was one of our good kids."

Another teacher, who taught Satterwhite in a class yesterday morning, described him as "a model student who never had to be told to do anything. He was a terrific kid, very polite," she said.

Rick Witcher, a senior, said he was in two classes with Satterwhite yesterday and he "didn't seem to have anything on his mind, he didn't seem to be bothered by anything."

The other shooting occurred about five hours earlier as Jackson was preparing to go to school at Calvin Coolidge High School, where he was a junior and a member of its basketball team, D.C. police reported.

Andre Jackson's brother, Edward (Junior) Jackson, 26, said he was asleep in the basement about 8:15 a.m. when his sister Beverly, 25, woke him to say she had heard three shots and had seen someone lying in the vestibule.

"I went upstairs and to the door to see who was in the vestibule, and it was Gerald," (Andre's middle name and the one used by family and close friends) Edward Jackson said.

Andre Jackson was pronounced dead a short time later at Washington Hospital Center of multiple gunshot wounds in the head, a hospital spokeswoman said.

Edward Jackson said his brother apparently had been getting ready to drive to school in his Datsun 280Z. One bookbag holding his books was in the car, he said, and the rear hatch was raised. Edward Jackson said his brother apparently had returned to the house to get another bookbag containing his tennis shoes.

Jackson's grandmother, Leona C. Barnes, said late last night that Jackson's mother, Virgie Ann Jackson, 32, was shot and killed in the same house in 1972. She said Jackson's father, Edward J. Jackson, was convicted in the slaying.

Barnes, 69, said she raised Andre Jackson, his brother Edward Jr., and his sisters Beverly and Sonia, 20, after their mother died. "All of them called me Momma," she said, her voice quavering.

Andre Jackson was a well-liked student, Barnes said. "He seemed to like school pretty good," she said. "And everybody liked him over at the school."

Coolidge Principal James E. Campbell said yesterday that "Everybody today was really kind of shocked."

He said Jackson, who enrolled in the school last year as a sophomore, "was a nice, congenial, hard-working student. He always had a very positive attitude."

A forward on the Coolidge varsity basketball team last year, Jackson had been a member of the Langley Junior High School team that compiled a 74-game winning streak in 1983 and 1984, Campbell said.

Kent Amos, who with his wife takes members of the Coolidge basketball team and cheerleading squad into his home as part of a tutoring program that provides a family atmosphere for the students, said Jackson died "senselessly."

"He was like a son to us," Amos said. "He was a fine young man that we we had been working with for the last two years. He died senselessly today.

"He wanted to use his basketball to give him an opportunity to go to college and change the course of his life," Amos said. "He then wanted to go back and help the kids who came behind him."

Amos said Jackson had often expressed his ambitions: "He wanted to be the first in his family to get a degree . . .[and] improve the economic and social conditions of his family and also to use whatever success that he had to help other needy families.