Question

Some pls help me with number 6

Answer 1

Answer:

m∠CBD = m∠CDB ⇒ proved

Step-by-step explanation:

Let us solve the question

∵ AB ⊥ BD ⇒ given

→ That means m∠ABD = 90°

∴ m∠ABD = 90° ⇒ proved

∵ ED ⊥ BD ⇒ given

→ That means m∠EDB = 90°

∴ m∠EDB = 90° ⇒ proved

∵ ∠ABD and ∠EDB have the same measure 90°

∴ m∠ABD = m∠EDB ⇒ proved

∵ m∠ABD = m∠ABC + m∠CBD

∵ m∠EDB = m∠EDC + m∠CDB

→ Equate the two right sides

∴ m∠ABC + m∠CBD = m∠EDC + m∠CDB

∵ m∠ABC = m∠EDC ⇒ given

→ That means 1 angle on the left side = 1 angle on the right side, then

   the other two angles must be equal in measures

∴ m∠CBD = m∠CDB ⇒ proved