Question

2. У трикутника DEC кут С прямий, zD = 25°. У трикутника PMK кут к прямий, ZM = 65°. Доведи, що дDEC = ДРМк, якщо DE = MP.

Answer 1

Ответ:

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Объяснение:

Answer 2

Given Information:

We are given the following information about two triangles:

Triangle DEC: - Angle C is a right angle (C = 90°). - Angle D is 25° (zD = 25°).

Triangle PMK: - Angle K is a right angle (K = 90°). - Angle M is 65° (ZM = 65°).

We need to prove that angle DEC is equal to angle DRMk, given that DE = MP.

Proof:

To prove that angle DEC is equal to angle DRMk, we will use the given information and apply the properties of triangles.

1. Given that DE = MP, we can conclude that triangle DEC is congruent to triangle PMK by the Side-Angle-Side (SAS) congruence criterion. This is because DE and MP are corresponding sides, and angle D and angle M are corresponding angles.

2. Since triangle DEC is congruent to triangle PMK, their corresponding angles are equal. Therefore, angle DEC is equal to angle PMK.

3. We are also given that angle C is a right angle (C = 90°) and angle K is a right angle (K = 90°). Since angle C and angle K are both right angles, we can conclude that angle DEC and angle DRMk are also right angles.

4. Since angle DEC and angle DRMk are both right angles, they are equal to each other.

Therefore, we have proved that angle DEC is equal to angle DRMk, given that DE = MP.

Note: The proof provided above is based on the given information and the properties of triangles.