Question

Given: YX = HX,
m∠Y=m∠H,
m∠ZXY=m∠KXH
Prove: YZ = HK

Answer 1

Answer:

Yes there are equal because of CPCT

Step-by-step explanation:

YX=HX ( SIDE)

ANGLE Y= ANGLE H ( ANGLE)

ANGLE X = ANGLE X ( ANGLE)

THEY ARE EQUAL BY AAS CONGRUENCE

SO , YZ = HK ARE EQUAL BY CPCT ( CORRESPONDING PART OF CONGRUENT TRIANGLE )

Answer 2

Proved that YZ = HK if YX = HX, m∠Y=m∠H and m∠ZXY=m∠KXH

Given:

• YX = HX,
• m∠Y=m∠H,
• m∠ZXY=m∠KXH

To Find:

• Prove: YZ = HK

Solution:

Step 1:

Compare ΔYXZ and ΔHXK

m∠Y=m∠H     ( given)

YX = HX         given

m∠ZXY=m∠KXH

Step 2:

Apply Angle-Side-Angle congruence criteria hence

ΔYXZ ≅ ΔHXK

Step 3:

Corresponding parts of congruent triangle are congruent hence

 YZ ≅  HK

Step 4:

Measure of congruent parts are equal hence

YZ =  HK

QED

Hence Proved

(Your Question is complete but missing figure which has been added)