Please explain given attachment In an isosceles triangle XYZ with X Y = XZ, XP bisects the base Y Z - Maths - Congruence of Triangles

Question

Please explain given attachment

Rashi Lokwani · Accepted Answer

Dear Student,

For proving that ∆XYP ≅ ∆ XZP, the SAS congruency criterion can be used
Proof:In ∆XYP and ∆ XZP:XY = XZ (given)∠XYP = ∠XZP (Angles opposite equal sides of an isosceles triangle are also equal)YP = ZP (because XP bisects YZ)Therefore, by SAS congruency criterion, ∆XYP ≅ ∆ XZP

Note: The RHS congruency criterion can also be used, because in an
isosceles triangle, the median is also the altitude

So, ∠XPY = ∠XPZ = 90 degreesand XY = XZand XP = XP (common) Therefore, ∆XYP ≅ ∆ XZP

Regards

Please explain given attachment Please explain given attachment In an isosceles triangle XYZ with X Y = XZ, XP bisects the base Y Z. Which of the following congruence criterion can be used to conclude that AXYP XVZP? RHS B. c. D. SAS ASA None of these

Please explain given attachment

Please explain given attachment In an isosceles triangle XYZ with X Y = XZ, XP bisects the base Y Z. Which of the following congruence criterion can be used to conclude that AXYP XVZP? RHS B. c. D. SAS ASA None of these