Problem

下列四个命题中正确命题的个数是() (1) 三点确定一个平面 (2) 若点P不在平面 $a$ 内, $A B C$ 三点都在平面 $a$ 内, 则P, $A, B, C$ 四点不共面 (3) 两两相交的三条直线在同一平面内 (4) 两组对边分别相等的四边形是平面图形. A. 0 B. 1 C. 2 D. 3

Solution

Step 1 :Analyze each statement and determine if it is true or false:

Step 2 :(1) 三点确定一个平面 (Three points determine a plane) - True

Step 3 :(2) 若点P不在平面 $a$ 内, $A B C$ 三点都在平面 $a$ 内, 则P, $A, B, C$ 四点不共面 (If point P is not on plane $a$, and points $A, B, C$ are on plane $a$, then points P, $A, B, C$ are not coplanar) - True

Step 4 :(3) 两两相交的三条直线在同一平面内 (Three lines that intersect pairwise are in the same plane) - True

Step 5 :(4) 两组对边分别相等的四边形是平面图形 (A quadrilateral with two pairs of equal opposite sides is a plane figure) - True

Step 6 :Count the number of true statements: 3

Step 7 :\(\boxed{\text{D. 3}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/26039/

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