Question

Match the statements with their values. Tiles when ΔABC is an isosceles triangle with when and ΔABC is an isosceles triangle with when and ΔPQR is an isosceles triangle with when and points D and E are the midpoints of and , respectively, in ΔABC Pairs 55° arrowBoth 180° arrowBoth 45° arrowBoth 30° arrowBoth

Answer 1

In an isosceles triangle, two sides are equal in length and two angles are equal in measure. The angles in an isosceles triangle can be determined based on the given information. The statements can be matched with their corresponding values.

Step-by-step explanation:

In an isosceles triangle, two sides are equal in length and two angles are equal in measure.

When ΔABC is an isosceles triangle with AB = AC, the angles opposite the equal sides, ∠B and ∠C, are also equal. Therefore, the statement can be matched with the value '55° arrowBoth'.

When ΔABC is an isosceles triangle with ∠A = ∠B, the two equal angles are both 45 degrees. Therefore, the statement can be matched with the value '45° arrowBoth'.

When ΔPQR is an isosceles triangle with PQ = QR, the angles opposite the equal sides, ∠P and ∠R, are also equal. Therefore, the statement can be matched with the value '30° arrowBoth'.

Points D and E are the midpoints of AB and AC, respectively, in ΔABC. This means that DE is parallel to BC and divides it into two equal parts. Therefore, the statement can be matched with the value '180° arrowBoth'.

Answer 2

For an isosceles triangle angles ABC=ACB=35
Let the angle ADB be x
then ADC is 180-x
as AD is median so BD=CD
and for isosceles triangle AB=AC
so AB/AC=BD/CD=1
By angle bisector theorem
BAD=CAD=y (just take it)
for an triangle BAD 35+x+y=180...(1)
for an triangle DAC 35+180-x+y=180...(2)
35+y=x
therefore
35+34+y+y=180
2y+70=180
2y=100
y=55
therefore angle BAD=CAD=55