Question

Drag the tiles to the correct boxes to complete the pairs.

Match the statements with their values.

1.m ∠ABC + m∠BAC + m∠ACB
when ΔABC is an isosceles triangle with

2. m∠ABC when m∠BAC = 70°
and ΔABC is an isosceles triangle with

3. m∠QPR when m∠QRP = 30°
and ΔPQR is an isosceles triangle with

4. m∠BDE when m∠BAC = 45°
and points D and E are the midpoints of
and , respectively, in ΔABC

Pairs:
1. 55°
2. 180°
3. 45°
4. 30°

Answer 1

In an isosceles triangle, the sum of its angles is 180 degrees. The angles in an isosceles triangle are equal. In an isosceles triangle, the base angles are equal to each other. In triangle ABC, if the angle BAC is given and points D and E are the midpoints, the corresponding angle BDE will be equal. Option 3 is correct.

Step-by-step explanation:

1. For an isosceles triangle ΔABC, the sum of its angles is always 180 degrees. Therefore, we can say that m∠ABC + m∠BAC + m∠ACB = 180 degrees. So, the value for this statement is 180 degrees.

2. When m∠BAC is given as 70 degrees in an isosceles triangle ΔABC, both m∠ABC and m∠ACB will be equal because of the property of isosceles triangles. Therefore, the value for this statement is 70 degrees.

3. Similar to the previous statement, when m∠QRP is given as 30 degrees in an isosceles triangle PQR, m∠QPR will also be 30 degrees because of the property of isosceles triangles. So, the value for this statement is 30 degrees.

4. In triangle ABC, if m∠BAC is given as 45 degrees and points D and E are the midpoints of AB and AC respectively, then m∠BDE will also be 45 degrees. This is because the line segment DE is parallel to the line segment BC and m∠BAC and m∠BDE are alternate interior angles. Therefore, the value for this statement is 45 degrees.