
817 S.W.2d 535 (1991)
STATE of Missouri, Respondent,
v.
Mark SEATON, Appellant.
No. 58342.
Missouri Court of Appeals, Eastern District, Division Five.
August 6, 1991.
Motion for Rehearing and/or Transfer Denied September 23, 1991.
Application to Transfer Denied November 19, 1991.
*536 William L. Webster, Atty. Gen., Joan F. Edwards, Asst. Atty. Gen., Jefferson City, for respondent.
Susan Lynn Hogan, Asst. Appellate Defender, Kansas City, for appellant.
Motion for Rehearing and/or Transfer to Supreme Court Denied September 23, 1991.
SIMON, Judge.
Appellant, Mark Seaton, appeals his convictions of forcible rape, Section 566.030 RSMo. (1986), and kidnapping, Section 565.110 RSMo. (1986), following a jury trial in St. Louis County. He was found to be a persistent sexual offender under Section 558.018 RSMo. (1986), and was sentenced to a term of 50 years on the rape count, and 15 years on the kidnapping count to run consecutively.
Appellant raises three points on appeal claiming the trial court erred in: (1) overruling appellant's pretrial motion to dismiss and overruling appellant's motions for *537 judgment of acquittal at the close of the state's case and at the close of all the evidence because the state failed to establish that the rape occurred in St. Louis County, thereby denying appellant the right to a trial by jury in the state and district wherein the charged crime was allegedly committed as guaranteed by the United States and Missouri Constitutions; (2) allowing the state to introduce the testimony of S.T. regarding an uncharged rape by appellant because such testimony violated the rule against admissibility of evidence of other crimes and did not fall under any exceptions to the rule; (3) submitting instruction number 4, MAI-CR3d 302.04, to the jury because that instruction violated appellant's due process rights as guaranteed by the United States and Missouri Constitutions, in that the instruction's definition of proof beyond a reasonable doubt as proof that leaves the jurors "firmly convinced" of defendant's guilt diminishes the meaning of proof beyond a reasonable doubt. We affirm.
Since appellant challenges the sufficiency of the evidence in one of his three points on appeal, we consider the facts and all reasonable inferences in the light most favorable to the verdict and reject all contrary evidence and inferences. State v. Spiller, 778 S.W.2d 825, 826[1] (Mo.App. 1989).
On the night of August 13, 1988, the victim was driving from her boyfriend's house in St. Charles County to her home in Alton, Illinois. Just north of the intersection of Highways 67 and 367, in St. Louis County, she noticed a motorist, later identified as appellant, behind her flashing his headlights. She pulled over to the shoulder of the road and appellant pulled over behind her. Appellant got out of his car and began looking at the rear of her car. Appellant told the victim that there were sparks coming from the back of her car. She got out of her car and walked towards the back of it. Appellant again told the victim he had noticed sparks, examined the right rear tire, and got on the ground, supposedly working underneath the car. Appellant then explained what he thought was wrong with the car, and she said she would have her mechanic look at it when she got home. Appellant asked her if she had any tools. When she said she didn't, appellant obtained a screwdriver from his car to again apparently work underneath the car. Appellant had her pull the car forward and back, supposedly to check for sparks, and told her he heard a noise coming from the car.
At some point, she gave appellant a beach towel with which to wipe his hands. She thanked appellant and initiated a handshake but appellant stalled and looked again at the car. When she indicated she was going to leave appellant initiated a handshake. When she extended her hand to shake appellant's, appellant punched her in the ribs, knocking her across the shoulder of the road. After a struggle, appellant wrapped the beach towel around her head and face, and forced her into his car, all the while threatening to harm her with a knife. However, she never saw a knife.
In his car, appellant forced her to keep her head down on the front seat. After driving around and making several turns, appellant stopped the car on a gravel road, forced her out of the car, pushed her onto the hood of the car, removed her pants and underwear, and raped her from behind. Appellant then pulled up her pants and put her back in the car. The towel remained over her head the whole time.
Appellant then drove around for a while longer, eventually dropped her off at her car, and drove away. She drove to Alton, Illinois and reported the incident to a police officer there. She was taken to St. Joseph's Hospital in Alton, and then to Christian Northeast Hospital in St. Louis County where she was examined by a doctor.
She described appellant's car as a green Chevelle with a split in the front seat, identified the car after it was obtained by police, and later identified photos of the car at trial. She also identified appellant in a lineup in Franklin County, and at trial, as her assailant.
In his first point, appellant claims the victim did not know where the actual rape took place because her car stopped near the border of St. Louis and St. Charles counties, *538 and she was unable to see where appellant took her when he drove around for several minutes before stopping on the gravel road where the rape occurred. Hence, appellant claims, the evidence was insufficient for the jury to find that the rape occurred in St. Louis County.
Since appellant is guaranteed the right to a public trial in the county in which the offense was committed, venue must be proved. Mo. Const. art. I, Section 18(a), State v. Stiles, 706 S.W.2d 944, 947[2, 3] (Mo.App.1986). Venue is not, however, an integral part of an offense and thus need not be proven beyond a reasonable doubt or by direct evidence, but may be inferred from all the evidence. State v. Lingar, 726 S.W.2d 728, 732[1, 2] (Mo. banc), cert. denied, 484 U.S. 872, 108 S.Ct. 206, 98 L.Ed.2d 157 (1987). The standard for review of an issue of venue is whether the jury could reasonably infer from the facts and circumstances that the crime with which the defendant is charged occurred within the trial court's jurisdiction. Id. Venue is proper in any county where any element of the crime occurred. Section 541.033(2), RSMo. (1986). Jackson v. State, 736 S.W.2d 515, 516[2] (Mo.App. 1987).
In determining the sufficiency of evidence of venue, appellate courts may take judicial notice of the official highway map of the State of Missouri. State v. Stiles, supra, at 947[4]. Here, the record supplies ample evidence from which it could be inferred that at least one element of both rape and kidnapping occurred in St. Louis County. The victim testified that she stopped her car south of the border between St. Louis County and St. Charles County. According to the official highway map of the State of Missouri this location is in St. Louis County. She testified that it was there that appellant punched her in the ribs, wrapped the towel on her head, and forced her physically and by threat of bodily harm into his car. The force, as an element of the crime of rape, was clearly applied to her in her initial abduction from the side of the highway in St. Louis County. See, State v. Burnside, 527 S.W.2d 22, 25[4] (Mo.App.1975). The same is true for appellant's removal of the victim without her consent from the place where he found her in St. Louis County, an element of the crime of kidnapping. Thus, the evidence was sufficient to establish proper venue in St. Louis County. Point denied.
In his second point, appellant contends the trial court erred in admitting the testimony of another woman, S.T., because her testimony was inadmissible evidence of other crimes. S.T. testified that in January of 1989 she was driving home late at night by herself when she noticed a motorist behind her flashing his headlights. She pulled over to the side of the road and the other motorist pulled up behind her. A man got out of the other car, and told her that there were sparks coming from underneath her car. The man said he would follow her and let her know if the sparks got any worse. The man followed her for a while and when she made a turn he flashed his lights a second time. She again pulled over and the man told her that the sparks were bad at that time. She pulled over in a nearby commuter lot so the man could look at her car. The man bent down as if examining the wheel of the car. At one point, she got back in her car but got out because the man continued to look at her car as if he was concerned. When she got back out the man grabbed her and dragged her back to his vehicle, which was a small pickup truck. He pushed her into the truck, forced her to keep her head down, and threatened her with a knife. The man drove to a cornfield, told her to take off her clothes and lay on her stomach, and proceeded to have sex with her from behind. At one point she was able to get out of the truck. She ran across the cornfield but the man caught her, dragged her back to the truck, pushed the front of her body against the truck, and tried again to penetrate her from behind but did not. The man again had sex with her inside the truck.
Eventually, the man allowed her to put her clothes on, drove her back near her car, and dropped her off. She reported the incident to the police and later identified the man in a photo lineup. During her testimony in the trial of the present case she identified appellant as her assailant.
Appellant argues that the admission of S.T.'s testimony was in violation of the rule *539 against admitting proof of other crimes. Generally, evidence of other crimes is inadmissible as violative of a defendant's right to be tried for the offense for which he is charged, unless the evidence has some legitimate tendency to establish the defendant's guilt of the charge for which he is on trial. State v. Reese, 364 Mo. 1221, 274 S.W.2d 304, 307[1] (banc 1954). Evidence of other crimes is competent to prove the specific crime charged when it tends to establish motive, intent, identity, absence of mistake or accident, or part of a common scheme or plan, Id., and is thus admissible if the probative value outweighs the prejudicial effect. State v. Brooks, 810 S.W.2d 627 (E.D.Mo.1991).
Here, one of the prosecution's stated reasons for offering the evidence in question was that it was relevant to show the identity of appellant as the perpetrator of the offenses charged through the similarity of method of operation in each instance. "Similarity of conduct, the so called modus operandi exception is based on its relevance toward proving the issue of identification. The fact that the same crime was committed in the same fashion with the same specific details lends logically to the conclusion that the two crimes were committed by the same person. This exception is usually limited to conduct of such an unusual or distinctive nature as to point almost unerringly to a single individual." State v. Lachterman, 812 S.W.2d 759 (E.D.Mo.1991).
Here, appellant in both instances flashed his headlights to get the attention of a lone female motorist, got her to pull over, told her there were sparks coming from the back of her car, and pretended to examine or fix the car. Appellant would then violently abduct the woman, keep her head down in the car while driving to a secluded location, threaten bodily harm with a knife, have sexual intercourse with her from behind, then drive back and drop her off near her car. We find appellant's conduct sufficiently unusual and distinctive so as to allow the introduction of evidence of the crimes as appellant's "handiwork", thereby establishing appellant's identification as the perpetrator. The evidence had a legitimate tendency to establish appellant's connection with the offense charged. See, State v. Young, 661 S.W.2d 637, 639-40[6-8] (Mo.App.1983). "The trial court is vested with broad discretion in ruling questions of relevancy of evidence and, absent a clear showing of abuse of that discretion, the appellate court should not interfere with the trial court's ruling." State v. Brown, 718 S.W.2d 493, 493-4[1] (Mo. banc 1986). Since the evidence here was relevant as to appellant's identity, the trial court was within its discretion to admit it.
Moreover, the admission of S.T.'s testimony was proper because of appellant's challenges, during cross-examination, to the present victim's ability to positively identify appellant as her attacker. "If the identity of the accused is established by other evidence and is therefore no longer an issue, it is improper to admit evidence of other crimes on the theory of proving identity." State v. Reese, supra, 274 S.W.2d at 307[2]. Here, appellant repeatedly challenged the victim's description of her attacker, which she gave to police after the incident, in order to keep the attacker's identity in question. Thus, the probative value of S.T.'s testimony as to the attacker's identity was important to the state's case. While the evidence was incriminating and therefore prejudicial by definition, State v. Shaw, 636 S.W.2d 667, 672[6] (Mo. banc 1982), it was admissible. Point denied.
In his final point, appellant claims the trial court erred in submitting to the jury the "reasonable doubt" instruction, MAI-CR3d 302.04, which defines proof beyond a reasonable doubt as proof which leaves the jury "firmly convinced of the defendant's guilt". Appellant did not object to the instruction at trial and asks that his claim be reviewed for plain error. Appellant contends this instruction diminishes the meaning of proof beyond a reasonable doubt to an unconstitutionally low standard, violating his right to due process.
As appellant acknowledges in his brief, the constitutionality of the language used in MAI-CR3d 302.04 was upheld in State v. Antwine, 743 S.W.2d 51, 62[12] (Mo. banc 1987), cert. denied, 486 U.S. 1017, 108 S.Ct. 1755, 100 L.Ed.2d 217 (1988). However, appellant claims the recent case of Cage v. *540 Louisiana, ___ U.S. ___, 111 S.Ct. 328, 112 L.Ed.2d 339 (1990), mandates reversal of his conviction. In Cage, the Supreme Court held that the Louisiana instruction equating "reasonable doubt" with "grave uncertainty" and "actual substantial doubt", and requiring "not an absolute or mathematical certainty, but a moral certainty" that the defendant was guilty, was contrary to due process.
MAI-CR3d 302.04 contains no such language, nor any similar language, as that ruled on in Cage. Thus, following Antwine, supra, we find the language in the instruction did not unconstitutionally diminish the meaning of proof beyond a reasonable doubt as required by the Due Process Clause. See also, State v. Turner, 810 S.W.2d 92 (Mo.App.1991). Point denied.
Judgment affirmed.
CARL R. GAERTNER, C.J., and CRANE, J., concur.
