Please help Match the picture to the reason that would prove the triangles congruent.

Options:
NONE
ASA
SSS
SAS
AAS
HL

Option (6). HL

Step-by-step explanation:

Given:

From the right triangles ΔBAC and ΔBDC,

AC ≅ CD

∠A = ∠D = 90°

To Prove:

ΔBAC ≅ ΔBDC

            Statements                       Reasons

1). AC ≅ DC                        1). Given

2). BC ≅ BC                       2). Reflexive property

3). ΔABC ≅ ΔBDC            3). By HL property of congruence of right triangles

Therefore, Option (6) HL will be the correct option.                              

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.