(CNN) -- A man sought in the slayings of a woman and her four young children in Oklahoma was arrested Tuesday night after a car chase in Texas, authorities said.



Joshua Steven Durcho was arrested Tuesday after a car chase with police.



Joshua Steven Durcho was arrested in Waco, Texas, after a Texas Department of Public Safety trooper tried to stop the car Durcho was driving because the trooper suspected a drunk driver, according to Erin Mangrum of the Canadian County, Oklahoma, sheriff's office.



The trooper checked the vehicle tag on the car and it matched the tag being sought by Oklahoma police, Mangrum said.



Mangrum said Durcho's car sped off, but he later wrecked the vehicle, and Durcho was taken into custody.



Durcho suffered minor injuries in the accident, Mangrum said.



Officers found the bodies of Summer Rust, 25, and her children Monday in their apartment in El Reno, about 30 miles west of Oklahoma City. Rust's daughter Evynn was 3, son Teagin was 4, and daughters Autumn and Kirsten were both 7.



Durcho is believed to have taken the slain woman's car, the Oklahoma State Bureau of Investigation said.



CNN affilate KOCO reported that Durcho had been spotted Monday night in Clinton, Oklahoma. His image was captured by surveillance cameras, the affiliate said, quoting police.



Authorities would not reveal how Rust and her children were killed, pending the outcome of autopsies. Rust's mother, Susan Rust of Carson City, Nevada, said her daughter had been shot, but she did not know how her grandchildren had been killed. Watch authorities name Durcho as the suspect »



Susan Rust said her daughter was loving and outgoing but tended to get involved with the wrong men.



Durcho was unemployed and had been living with Summer Rust and her children, the mother said. Police were asked to check up on the family because Rust and Durcho had had a fight, she said.



Summer Rust attended Redlands Community College in El Reno, where she majored in legal assistant training, according to school officials. Rust's mother said she was retraining after losing her job in casino security several months ago.



"Summer was very bright, very outgoing, had a positive attitude and was very determined to complete her education," Julie Lamb of the college told CNN Radio.



Lamb heads a student support program on campus. The school brought in grief counselors Tuesday to help students affected by the killings. Domestic violence groups also reached out to the students.



A friend posting online described Summer Rust as "fun-loving" and "a little crazy kind of person" who was also very smart.



"Her children were beautiful, funny and always cheerful and sometimes a little wild. They were a great bunch of kids and they loved each other very much. They were proud of their mom for going back to school," the friend said.



"She was going to make a better life for her family. I can't believe something like this could happen to her and the kids. ... I will miss her silliness and her smile. I will miss them all."
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