The defendant appeals from a judgment of conviction, rendered after a jury trial, of two counts of sexual assault in the first degree in violation of General Statutes § 53a-70 (a) (2), and two counts of risk of injury to a child in violation of General Statutes § 53-21. On appeal, the defendant claims the trial court violated his right of confrontation when it improperly limited cross-examination of a state’s witness regarding her possible bias toward him. We disagree and affirm the judgment of the trial court.
The jury could reasonably have found the following facts. During the months of November and December, 1989, the victims, a five year old girl and a three year old boy, spent weekends visiting with their father at the home of the defendant, their paternal grandfather.1 Upon returning to their mother’s home after one of their weekend visits, the five year old complained to her mother that her grandfather had forced her to perform various sexual acts with both him and her younger brother. The police were contacted and the children *83were interviewed by Detective Robert Drozynski of the Norwich police department at which time the five year old gave the detective a detailed description of the “bad things” the defendant had done to her. The defendant was subsequently arrested and charged with two counts each of sexual assault in the first degree and risk of injury to a child.
The defendant claims the trial court improperly interfered with his right to cross-examine witnesses. It is undisputed that the defendant is entitled fairly and fully to confront and to cross-examine the witnesses against him. U.S. Const., amends. VI, XIV; Conn. Const., art. I, § 8; Davis v. Alaska, 415 U.S. 308, 318, 94 S. Ct. 1105, 39 L. Ed. 2d 347 (1974); State v. Maldonado, 193 Conn. 350, 356, 478 A.2d 581 (1984); State v. Hackett, 182 Conn. 511, 517, 438 A.2d 726 (1980). Neither constitution, however, requires that the defendant be permitted to present every piece of evidence he wishes. Chambers v. Mississippi, 410 U.S. 284, 302, 93 S. Ct. 1038, 35 L. Ed. 2d 297 (1973); State v. Kelly, 208 Conn. 365, 376, 545 A.2d 1048 (1988). If the proffered evidence is not relevant, the defendant’s right of confrontation is not affected and the evidence should be excluded. State v. Kelly, supra.
As a general principle, evidence is relevant if it has a tendency to establish the existence of a material fact. One fact is relevant to another fact whenever, according to the common course of events, the existence of the one, taken alone or in connection with other facts, renders the existence of the other either certain or more probable. State v. Cassidy, 3 Conn. App. 374, 383, 489 A.2d 386, cert. denied, 196 Conn. 803, 492 A.2d 1239 (1985); see also State v. Mastropetre, 175 Conn. 512, 517, 400 A.2d 276 (1978) and State v. Lombardo, 163 Conn. 241, 243, 304 A.2d 36 (1972).
*84On cross-examination, the defendant attempted to demonstrate bias on the part of the victims’ mother, and to impeach her credibility by introducing evidence that the defendant had previously threatened to initiate a criminal action against her for the theft of various tools from behind his house. The state’s attorney objected to each attempt on the ground of relevancy. The defendant failed to make an offer of proof as to the relevance of this testimony, and the court sustained each objection.2
It is the appellant’s burden to ensure that we are provided with an adequate appellate record to support his claim. Barra v. Ridgefield Card & Gift Gallery, Ltd., 194 Conn. 400, 407, 480 A.2d 552 (1984). The defendant in the present case has not met this burden. If he wanted to provide this court with an adequate appellate record, he should have presented an offer of proof. “ ‘An offer of proof, properly presented, serves three purposes. First, it should inform the court of the legal *85theory under which the offered evidence is admissible. Second, it should inform the trial judge of the specific nature of the offered evidence so the court can judge its admissibility. Third, it thereby creates a record adequate for appellate review.’ ” State v. Conrod, 198 Conn. 592, 597, 504 A.2d 494 (1986), citing Mad River Orchard, Inc. v. Krack Corporation, 89 Wash. 2d 535, 537, 573 P.2d 796 (1978).
The defendant concedes that no offer of proof was made. He asserts, however, that the record reveals sufficient indicia of the legal theory, i.e., transferred bias, under which the evidence was offered, to warrant introduction of the evidence in the absence of a formal offer of proof. We find no facts that warrant importing the proffered evidence into the case. All that the record reveals is that the defendant attempted to offer evidence of the defendant’s accusation of theft against the mother of the children and an objection was sustained as to relevancy. This fact standing alone, as it must without an offer of proof, does not have any bearing on any material fact in this case. The defendant introduced no evidence to corroborate his theory that any bias on the part of the children’s mother was in fact transferred to her five year old daughter. Defense counsel was free to inquire of the daughter whether she was influenced in any way by her mother. He failed to do so.3
“The significant gap in the record . . . limits our review and presents obstacles to reviewing the defendant’s claim of error on this appeal.” Barra v. Ridgefield Card & Gift Gallery, Ltd., supra. In the absence of an appropriate offer of proof, this court cannot speculate as to what line of questioning defense counsel intended to follow. A claim on appeal cannot be based on an *86assumption that the trial court acted improperly. Id., 407-408. Without an adequate record on which to review the rulings of the trial court, this court must assume that the trial court acted properly. Jacobson v. Jacobson, 177 Conn. 259, 267, 413 A.2d 854 (1979); Johnson v. Newell, 160 Conn. 269, 277, 278 A.2d 776 (1971). Thus, we find no violation of the defendant’s right of confrontation.
The judgment is affirmed.
In this opinion the other judges concurred.
The victims’ parents had recently separated. Their father was residing on a temporary basis with his parents, the defendant and his wife, during the time period in question.
The questions and subsequent colloquys were as follows:
“Q. In November of 1989 did my client accuse you [the victims’ mother] of stealing tools that were located behind—
“A. No.
“Mr. Pannone: I will object to the question on the grounds of relevance. I don’t see where it is relevant at all. It is beyond the scope of direct examination.
“The Court: You said November of ’89. That is after this.
“Mr. Perry: Actually, Your Honor, it is at the very beginning of when these alleged events occurred.
“The Court: I will sustain the objection.
“Mr. Perry: Exception please, Your Honor.
“The Court: Exception noted.”
[Cross-examination by Mr. Perry continuing]:
“Q. Did you [the victims’ father] ever have occasion to hear your father mention to you about a theft of tools from behind the house?
“Mr. Pannone: Again, Your Honor, I am going to object as to the relevance to that question. It is attempting to raise a collateral issue.
“The Court: Sustained.
“Mr. Perry: Exception.
“The Court: Exception noted.”
This failure, whether through inadvertence or for tactical reasons, is the sole basis on which the importance of the mother’s testimony is premised.