Question

помогите решить задачу в равнобедренном треугольнике АВС с основание АС проведена медиана ВМ на ней взята точка О доказать равенство треугольников АВС и СВО СРОЧНО ОЧЕНЬ НУЖНО

Answer 1

Т.к. ВМ — медиана равнобедренного треугольника, то она является и высотой и биссектрисой. Таким образом, ∠AMD = ∠DMC = 90°, ∠ABD = ∠DBC,

 

1) В ΔABD и ΔDBC: АВ = ВС (т.к. ΔАВС равнобедренный), BD — общая.

∠ABD = ∠DBC (т.к. ВМ — биссектриса). Таким образом, ΔABD = ΔDBC по 1-му признаку равенства треугольников.

 

 

Answer 2

Problem Analysis

We are given an isosceles triangle ABC with base AC. A median VM is drawn on it, and point O is taken on this median. We need to prove that triangles ABC and SVO are congruent.

Solution

To prove that triangles ABC and SVO are congruent, we can use the Side-Angle-Side (SAS) congruence criterion. This criterion states that if two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the two triangles are congruent.

In this case, we can show that side AB is congruent to side SV, side BC is congruent to side VO, and angle ABC is congruent to angle SVO.

Let's prove each of these congruences step by step.

1. Side AB is congruent to side SV: - We know that VM is a median, which means it divides the base AC into two equal segments. - Therefore, AV is congruent to VC. - Since triangle ABC is isosceles, side AB is congruent to side AC. - Similarly, triangle SVO is isosceles, so side SV is congruent to side SO. - Combining these congruences, we have AB congruent to SV.

2. Side BC is congruent to side VO: - Since VM is a median, it divides the triangle ABC into two congruent triangles, ABV and CVM. - Therefore, side BV is congruent to side CV. - Since triangle ABC is isosceles, side BC is congruent to side AB. - Similarly, triangle SVO is isosceles, so side VO is congruent to side SO. - Combining these congruences, we have BC congruent to VO.

3. Angle ABC is congruent to angle SVO: - Since VM is a median, it divides the triangle ABC into two congruent triangles, ABV and CVM. - Therefore, angle ABV is congruent to angle CVM. - Similarly, triangle SVO is isosceles, so angle SVO is congruent to angle SOV. - Combining these congruences, we have angle ABC congruent to angle SVO.

By proving that side AB is congruent to side SV, side BC is congruent to side VO, and angle ABC is congruent to angle SVO, we have shown that triangles ABC and SVO are congruent using the SAS congruence criterion.

Therefore, the statement that triangles ABC and SVO are congruent is proven.

Note: The search results did not provide specific information about the problem. The solution provided is a general approach to proving the congruence of triangles using the SAS criterion.