Math

Question等腰三角形一个底角为 45 度,问这个三角形的类型是?(1) 锐角 (2) 直角 (3) 钝角 (4) 无法确定

Studdy Solution

STEP 1

Assumptions1. The triangle is an isosceles triangle, which means two of its sides are equal in length. . One of the base angles of the triangle is45 degrees.

STEP 2

In an isosceles triangle, the base angles are always equal. Therefore, the other base angle is also45 degrees.
Other base angle=45\text{Other base angle} =45^{\circ}

STEP 3

The sum of the angles in a triangle is always180 degrees. We can use this fact to find the third angle of the triangle.
Third angle=180First base angleSecond base angle\text{Third angle} =180^{\circ} - \text{First base angle} - \text{Second base angle}

STEP 4

Plug in the values for the first and second base angles to calculate the third angle.
Third angle=1804545\text{Third angle} =180^{\circ} -45^{\circ} -45^{\circ}

STEP 5

Calculate the third angle.
Third angle=1804545=90\text{Third angle} =180^{\circ} -45^{\circ} -45^{\circ} =90^{\circ}The third angle is90 degrees, which is a right angle. Therefore, the triangle is a right triangle.

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