All SSAT Upper Level Math Resources
Example Questions
Example Question #1 :How To Find If Right Triangles Are Congruent
Given:
, whereis a right angle;;
, whereis a right angle and;
, whereis a right angle andhas perimeter 60;
, whereis a right angle andhas area 120;
, whereis a right triangle and
Which of the followingmustbe a false statement?
All of the statements given in the other responses are possible
has as its leg lengths 10 and 24, so the length of its hypotenuse,, is
我ts perimeter is the sum of its sidelengths:
我ts area is half the product of the lengths of its legs:
andhave the same perimeter and area, respectively, as; also, betweenand, corresponding angles are congruent. In the absence of other information, none of these three triangles can be eliminated as being congruent to.
However,and. Therefore,. Since a pair of corresponding sides is noncongruent, it follows that.
Example Question #1 :How To Find If Right Triangles Are Congruent
Given:andwith right anglesand;.
Which of the following statementsalone, along with this given information, would prove that?
我)
我我)
我我我)
我or III only
我我or III only
我我我only
我or II only
Any of I, II, or III
Any of I, II, or III
;since both are right angles.
Given that two pairs of corresponding angles are congruent and any one side of corresponding sides is congruent, it follows that the triangles are congruent. In the case of Statement I, the included sides are congruent, so by the Angle-Side-Angle Congruence Postulate,. In the case of the other two statements, a pair of nonincluded sides are congruent, so by the Angle-Angle-Side Congruence Theorem,. Therefore, the correct choice is I, II, or III.
Example Question #3 :How To Find If Right Triangles Are Congruent
, whereis a right angle,, and.
Which of the following is true?
None of the statements given in the other choices is true.
has area 100
has perimeter 40
has area 100
, and corresponding parts of congruent triangles are congruent.
Sinceis a right angle, so is.and; since, it follows that.is an isosceles right triangle; consequently,.
是45-45-90三角形的斜边长度. By the 45-45-90 Triangle Theorem, the length of each leg is equal to that of the hypotenuse divided by; therefore,
is eliminated as the correct choice.
Also, the perimeter ofis
.
This eliminates the perimeter ofbeing 40 as the correct choice.
Also,消除是正确的选择,因为三angle is 45-45-90.
The area ofis half the product of the lengths of its legs:
The correct choice is the statement thathas area 100.
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