GMAT Official Guide Quantitative Review 2019_ Book

3.3 t Geometry

二

Y

卜尸尸——

d

In 45°-45°-90°triangles, the lengths of the sides are in the ratio 1:1: Ji. For example, in L1JKL,
叮L=2, then]K= 2 and KL= 2拉.In 30°-60°-90°triangles, the lengths of the sides are in the ratio
1: ✓

3

:2. For example, in丛立，ifXZ= 3, thenXY= 3✓

3

and YZ= 6.

The altitude of a triangle is the segment drawn from a vertex perpendicular to the side opposite that

vertex. Relative to that vertex and altitude, the opposite side is called the base.

The area of a triangle is equal to:

(the length of the altitude) X (the length of the base)

2

B

A D C

I• 8•I

BD=S

In MBC, BD is the altitude to base AC and AE is the altitude to base BC. The area of凶BC

is equal to

BDxAC 5x8 =-—=20.

2 2

The area is also equal to AExBC. If闷BCabove is isosceles and AB= BC, then altitude的bisects

2

the base; that is, AD= DC= 4. Similarly, any altitude of an equilateral triangle bisects the side to which

it is drawn.

D ,o^00 ·F

In equilateral triangle DEF, if DE= 6, then DG = 3 and EG = 3✓

3

. The area of t:iDEF is equal to
3 ✓

3

x6 = (^9) ✓^3.
2