Question

Помогите! Срочно! Очень нужен ответ!!!Из точек A и B на прямую a опущены перпендикуляры AC и BD, причем AC=BD. Докажите, что треугольник ACD равен треугольнику BDC.Пожалуйста помогите!

Answer 1

Треугольник ACD и  треугольник BDC прямоугольные , так как АС и BD перпендикуляры. У них АС=BD по условию, а сторона СD общая.
.треугольник ACD равен треугольнику BDC по двум катетам

Answer 2

Proof that triangle ACD is congruent to triangle BDC

To prove that triangle ACD is congruent to triangle BDC, we can use the fact that AC is equal to BD and the given information that AC and BD are perpendiculars dropped from points A and B, respectively, to the line segment AB.

Here's the step-by-step proof:

1. Given: AC = BD (given information) 2. AC and BD are perpendiculars dropped from points A and B, respectively, to the line segment AB (given information)

To prove: Triangle ACD is congruent to triangle BDC

Proof:

Step 1: Since AC and BD are perpendiculars dropped from points A and B, respectively, to the line segment AB, we can conclude that AB is the base of both triangles ACD and BDC.

Step 2: Since AC = BD, we can conclude that the lengths of the corresponding sides of triangles ACD and BDC are equal.

Step 3: Since AB is the base of both triangles ACD and BDC and the lengths of the corresponding sides are equal, we can conclude that the triangles have equal heights.

Step 4: Therefore, the areas of triangles ACD and BDC are equal.

Step 5: By the Side-Angle-Side (SAS) congruence criterion, if two triangles have equal areas and share two equal sides, they are congruent.

Step 6: Since triangles ACD and BDC have equal areas and share two equal sides (AC = BD), we can conclude that triangle ACD is congruent to triangle BDC.

Therefore, we have proved that triangle ACD is congruent to triangle BDC.

I hope this helps! Let me know if you have any further questions.