Respuesta :

thebecks

Answer:

The key is to prove that the triangles are congruent, then their corresponding parts are congruent.

Step-by-step explanation:

#5)

It it given that:

Angle CBD is congruent to angle CDB.

Angle BAE is congruent to angle DEA.

Triangle CBD is isosceles because it's base angles are equal. Therefore, segment CB is congruent to segment CD.

Triangle CAE is isosceles because it's base angles are equal. Therefore, segment CA is congruent to segment CE.

CA-CB=BA

CE-CD=DE

segment BD is congruent to segment DB.

Angle ABD is supplementary to angle CBD (180-angle CBD= angle ABD).

Angle EDB is supplementary to angle CDB (1980-angle CDB=angle EDB).

therefore, angle ABD=angle EDB.

Triangles ABD and EDB are congruent because of the Side-angle-side theorem.

Triangles ABD and EDB are congruent, segment AD is congruent to segment EB because corresponding legs of congruent triangles are congruent.

#6)

It is given that:

Angle EBC is congruent to angle ECB

Segment AE is congruent to segment DE.

Triangle BEC is iscsceles because it's base angles are equal. Therefore, segment EB is congruent to segment EC.

AE+EC=AC

DE+EB=DB

segment BC is congruent to segment CB.

Triangle BAC is congruent to triangle CDB because of the side-angle-side theorem.

Segment AD is congruent to segment DC because corresponding legs of congruent triangles are congruent.

mberisso

Answer:

Problem 5)

Step 1:  < CBD = <CDB Reason: given

Step 2: BC = CD  Reason: opposed sides in the isosceles triangle BCD

Step 3: < BAE = < DEA Reason: given

Step 4: AC = CE Reason: opposed sides in the isosceles triangle ACE

Step 5: triangle ACD  = triangle BCE Reason: angle <C is common, and equal sides shown above so use SAS theorem.

Step 6: AD =  BE Reason: third side in the equal triangles shown above.

Problem 6)

Step 1: < ECB = <EBC Reason: Given

Step 2> triangle BEC is isosceles Reason: has two equal angles

Step 3: BE = EC Reason: opposite sides in the isosceles triangle

Step 4: <DEC = < AED Reason: opposed by the vertex (vertical angles)

Step 5: AE = ED Reason: given

Step 6: triangle BAE = triangle EDC Reason SAS theorem

Step 7: side AB = side CD Reason: third side in the equal triangles