GMAT Math : Calculating whether right triangles are congruent

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Example Question #282 : Geometry

A right triangle has a height of $\displaystyle 5$ and a base of $\displaystyle 12$. In order for another triangle to be congruent, what must be the length of its hypotenuse?

Possible Answers:

$\displaystyle 12$

$\displaystyle 17$

$\displaystyle 13$

$\displaystyle 5$

$\sqrt{17}$ $\displaystyle \sqrt{17}$

Correct answer:

$\displaystyle 13$

Explanation:

In order for two triangles to be congruent, they must be identical. That is, the lengths of the corresponding sides of two congruent triangles must be equal. This means that in order for a triangle to be congruent to one with a height of $\displaystyle 5$ and a base of $\displaystyle 12$, its hypotenuse must be the same length as the hypotenuse of that triangle, which we can find using the Pythagorean Theorem:

$\displaystyle a^2+b^2=c^2$

$\displaystyle 5^2+12^2=c^2$

$c^2=169\rightarrow c=\sqrt{169}=13$ $\displaystyle c^2=169\rightarrow c=\sqrt{169}=13$

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Example Question #283 : Geometry

A given right triangle has a base of $\displaystyle 9$ and a height of $\displaystyle 12$. What must the base length of a congruent right triangle be?

Possible Answers:

$\displaystyle 9$

$\displaystyle 18$

None of the above.

$\displaystyle 12$

$\displaystyle 24$

Correct answer:

$\displaystyle 9$

Explanation:

In order for two right triangles to be congruent, the bases and heights must have identical lengths. Since we have a given right triangle with a base of $\displaystyle 9$, the congruent right triangle must also have a base of $\displaystyle 9$ .

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Example Question #3 : Calculating Whether Right Triangles Are Congruent

A given right triangle has a height of $\displaystyle 7$ and an acute angle of $42^{\circ}$ $\displaystyle 42^{\circ}$. What must the acute angle of a congruent right triangle be?

Possible Answers:

$21^{\circ}$ $\displaystyle 21^{\circ}$

$84^{\circ}$ $\displaystyle 84^{\circ}$

None of the above.

$45^{\circ}$ $\displaystyle 45^{\circ}$

$42^{\circ}$ $\displaystyle 42^{\circ}$

Correct answer:

$42^{\circ}$ $\displaystyle 42^{\circ}$

Explanation:

In order for two right triangles to be congruent, the hypotenuses and acute angles must be identical. Since we have a given right triangle with an acute angle of $42^{\circ}$ $\displaystyle 42^{\circ}$, the congruent right triangle must also have an acute angle of $42^{\circ}$ $\displaystyle 42^{\circ}$ .

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Example Question #4 : Calculating Whether Right Triangles Are Congruent

A given right triangle has a base of $\displaystyle 12$ and a height of $\displaystyle 5$. What must the base length of a congruent right triangle be?

Possible Answers:

$\displaystyle 12$

$\displaystyle 5$

None of the above.

$\displaystyle 10$

$\displaystyle 6$

Correct answer:

$\displaystyle 12$

Explanation:

In order for two right triangles to be congruent, the bases and heights must have identical lengths. Since we have a given right triangle with a base of $\displaystyle 12$, the congruent right triangle must also have a base of $\displaystyle 12$ .

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GMAT Math : Calculating whether right triangles are congruent

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #282 : Geometry

Example Question #283 : Geometry

Example Question #3 : Calculating Whether Right Triangles Are Congruent

Example Question #4 : Calculating Whether Right Triangles Are Congruent

All GMAT Math Resources

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