Question

СРОЧНО. Точки В и N лежат по одну сторону от прямой а. Перпендикуляры BR и ND к прямой а равны, а) Докажите, что ABRD=ANDR; б) найдите <BRN, если <BDR = 36°.​

Answer 1

Ответ:

а) Если диагонали четырехугольника равны, и это параллелограмм то он является прямоугольником.

Δ BRD=ΔNDR по углу ∠BRD=∠NDR=90° и двум сторонам этого угла

RD - общая сторона и BR=ND ⇒ BD= NR диагонали

BR║ND; ВN║RD так как тт. В и N находятся на одинаковом расстоянии от отрезка RD ⇒ BNRD прямоугольник

б) <BRN =<RND=<RBD=90-36=54°

Объяснение:

Answer 2

Problem Statement

We are given points B and N on one side of line a, and points R and D on the other side of line a. Perpendiculars BR and ND to line a are equal. We need to prove that quadrilateral ABRD is congruent to quadrilateral ANDR. Additionally, we need to find the measure of angle BRN if angle BDR is 36°.

Solution

a) To prove that quadrilateral ABRD is congruent to quadrilateral ANDR, we can use the SAS (Side-Angle-Side) congruence criterion. According to this criterion, if two sides and the included angle of one triangle are congruent to the corresponding sides and angle of another triangle, then the triangles are congruent.

In this case, we can see that: - Side AB is congruent to side AN because they are both perpendicular to line a and have the same length (given). - Side BR is congruent to side DR because they are both perpendicular to line a and have the same length (given). - Angle ABR is congruent to angle NDR because they are both right angles (perpendicular to line a).

Therefore, we have the congruence of corresponding sides and the included angle, which proves that quadrilateral ABRD is congruent to quadrilateral ANDR.

b) To find the measure of angle BRN, we can use the fact that the sum of the angles in a triangle is 180°. Since we know that angle BDR is 36°, we can find angle BRN by subtracting the measures of angles BDR and NDR from 180°.

Let's calculate it: - Angle BDR = 36° (given) - Angle NDR = 90° (perpendicular to line a)

Sum of angles in triangle BDR: 36° + 90° + angle BRN = 180°

Simplifying the equation: angle BRN = 180° - 36° - 90° angle BRN = 54°

Therefore, the measure of angle BRN is 54°.

Note: The given solution is based on the information provided in the problem statement. If there are any additional constraints or information, please let me know, and I will be happy to assist you further.