If the incircle is tangent to the hypotenuse AB at point P, then denoting the semi-perimeter as s, we have and, and the area is given by

If an altitude is drawn from the vertex with the right angle to the hypotenuse then the triangle is divided into two smaller triangles which are both similar to the original and therefore similar to each other.

If the " opposite " side has length x − 4 and the " adjacent " side has length 3, then the Pythagorean theorem tells us that the hypotenuse has length √(( x − 4 )< sup > 2 </ sup > + 3 < sup > 2 </ sup >)

* y and x: If y is a square and x is a square or twice a square, then each of a and b is a square or twice a square and the integer right triangle with legs and and hypotenuse would have two sides ( b and a ) each of which is a square or twice a square, with a smaller hypotenuse than the original triangle ( compared to ).

* z and x: If z is a square and x is a square or twice a square, again each of a and b is a square or twice a square and the integer right triangle with legs and and hypotenuse also would have two sides ( and ) each of which is a square or twice a square, and a smaller hypotenuse ( compared to.

If the length of the hypotenuse of a right triangle is 1, then the lengths of the legs are the sine and cosine of one of the angles.

If one leg of a right triangle has length 1, then the tangent of the angle adjacent to that leg is the length of the other leg, and the secant of the angle is the length of the hypotenuse.

* If and only if it is a right triangle, the circumcenter lies at the center of the hypotenuse.

If the circumstances are faced frankly it is not reasonable to expect this to be true.

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;

If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

If it is an honest feeling, then why should she not yield to it??

If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

If he is good, he may not be legal ; ;

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If the existent form is to be retained new factors that reinforce it must be introduced into the situation.

If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??

If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.

If he is a traditionalist, he is an eclectic traditionalist.

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

If it were not for the effect of destructive agencies, sawtimber growth would have been nearly twice as great as the 47 billion board feet in 1952.

If we have five problems whose solution we seek in relatively united fashion, then there are twice as many issues which, I judge, sharply divide us, intergroup relations practitioners and lay people.

If, for example, a string sounds the note C when plucked, a string twice as long will sound the same note an octave lower.

If the first team misses twice, the other team is awarded the opportunity to place the jack anywhere they choose within the prescribed zone.

If a player rolls two of the same number, called doubles, that player must play each die twice.

If we draw an ellipse twice as long as it is wide, and draw the circle centered at the ellipse's center with diameter equal to the ellipse's longer axis, then on any line parallel to the shorter axis the length within the circle is twice the length within the ellipse.

If objects are new from moment to moment so that one can never touch the same object twice, then each object must dissolve and be generated continually momentarily and an object is a harmony between a building up and a tearing down.

If the registered amount exceeded 10, 000 Derrik, he or she would receive an amount of twice as much.

If twice or three times that does not suffice, then not even the wealth of Croesus or of Persia will suffice.

If it is less than twice the

If an organism lives half as long as others of its species, but has twice as many offspring surviving to adulthood, its genes will become more common in the adult population of the next generation.

If rotations are also considered distinct, then the pentominoes from the first category count eightfold, the ones from the next three categories ( T, U, V, W, Z ) count fourfold, I counts twice, and X counts only once.

* If all clubs involved have played each other twice:

If the ball contacts the front wall so low as to bounce twice before it reaches the service line it is called a " kill " shot.

If a simple pendulum is suspended from the cusp of an inverted cycloid, such that the " string " is constrained between the adjacent arcs of the cycloid, and the pendulum's length is equal to that of half the arc length of the cycloid ( i. e. twice the diameter of the generating circle ), the bob of the pendulum also traces a cycloid path.

If this happened, Labor would have an effective 33 – 31 margin, would be able to pass supply if that was still an issue, and also could pass electoral redistribution laws ( which had been passed by the House, though twice defeated by the Senate ) that would give it an advantage at the next election.

If the satellite is more than twice as dense as the primary, as can easily be the case for a rocky moon orbiting a gas giant, then the Roche limit will be inside the primary and hence not relevant.

If the interest is credited once, at the end of the year, the value is $ 2. 00 ; but if the interest is computed and added twice in the year, the $ 1 is multiplied by 1. 5 twice, yielding $ 1. 00 × 1. 5² = $ 2. 25.

If the House twice passes the same bill, and the Senate twice fails to pass that bill ( either through rejection or through the passage of unacceptable amendments ), then the Governor-General may dissolve both Houses of Parliament simultaneously and call an election for the entire Parliament.

If the ship was safe, the bell would be rung twice ; if it had sunk, the bell would be rung once.

If a student, by his own study and mental force, reached the desired point which the musician's wizardry had made him see, he gained reliance in his own strength, knowing he would always find that point again even though he should lose his way once or twice, as everyone with an honest aspiration is liable to do.