Question

To verify the property of median on hypotenuse of right angle triangle. And how to write aim app and procedure ​

Answer 1

Step-by-step explanation:

(1) AD=DB //given, CD is the median to the hypotenuse

(2) CE=EB //construction

(3) DE is a midsegment //(1), (2) , Definition of a midsegment

(4) DE||AC //triangle midsegment theorem

(5) ∠DEB ≅ ∠ACE // corresponding angles in two parallel lines intersected by a transversal line (CE)

(6) m∠ACE=90° //given, ΔABC is a right triangle

(7) m∠DEB=90° //(5), (6), definition of congruent angles

(8) m∠DEC=180° – 90° = 90° // linear pair

(9) ∠DEB ≅ ∠DEC //(7),(8), definition of congruent angles

(10) DE=DE //common side, reflexive property of equality

(11) ΔDCE ≅ ΔDBE //(2), (9), (10) Side-Angle-Side postulate

(12) CD=DB // Corresponding sides in congruent triangles (CPCTC)

(13) DB= ½AB // Given, CD is the median to the hypotenuse

(14) CD= ½AB //(12) , (13), substitution