choose your answers from the drop - down menus.
a. a rhombus has 4 congruent sides, so segments ab, cb, ad, and cd are congruent.
b. segment db is congruent to segment db because segments are congruent to themselves.
c. triangle dab is congruent to triangle dcb by side - side - side triangle congruence theorem.
d. angle abd is congruent to angle cbd because corresponding parts of congruent triangles are congruent.
e. therefore, diagonal bd bisects angle abc because options: it divides the angle into 2 congruent angles, it divides the opposite side into 2 congruent segments, it divides the opposite angle into 2 congruent angles

Question

Accepted Answer

### Part a
# Explanation:
A rhombus is defined as a quadrilateral with all four sides congruent. So the number of congruent sides in a rhombus is 4.
## Step1: Recall the definition of a rhombus
A rhombus is a parallelogram with 4 congruent sides.
# Answer:
4 congruent sides

### Part b
# Explanation:
In a rhombus, a segment is congruent to itself by the Reflexive Property of Congruence. Here, segment $ DB $ is congruent to segment $ DB $ (itself).
## Step1: Apply the Reflexive Property
The Reflexive Property states that any geometric figure is congruent to itself. So segment $ DB $ is congruent to $ DB $.
# Answer:
$ DB $; $ DB $

### Part c
# Explanation:
To prove $ \triangle DAB \cong \triangle DCB $ in a rhombus:
- $ AB = CB $ (sides of a rhombus are congruent)
- $ AD = CD $ (sides of a rhombus are congruent)
- $ DB = DB $ (common side, Reflexive Property)

By the Side - Side - Side (SSS) Triangle Congruence Theorem, if three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.
## Step1: Identify the sides of the triangles
In $ \triangle DAB $ and $ \triangle DCB $, $ AB\cong CB $, $ AD\cong CD $, and $ DB\cong DB $.
## Step2: Apply the SSS congruence theorem
Since three pairs of sides are congruent, by SSS, $ \triangle DAB\cong\triangle DCB $.
# Answer:
Side - Side - Side

### Part d
# Explanation:
When two triangles are congruent ($ \triangle ABD\cong\triangle CBD $ from part c), their corresponding parts (angles, sides) are congruent. So $ \angle ABD\cong\angle CBD $ because corresponding parts of congruent triangles are congruent (CPCTC).
## Step1: Recall the CPCTC theorem
Corresponding Parts of Congruent Triangles are Congruent (CPCTC).
## Step2: Apply CPCTC to $ \triangle ABD $ and $ \triangle CBD $
Since $ \triangle ABD\cong\triangle CBD $, $ \angle ABD $ (corresponding to $ \angle CBD $) is congruent to $ \angle CBD $.
# Answer:
corresponding parts of congruent triangles are congruent

### Part e
# Explanation:
A bisector of an angle divides the angle into two congruent angles. Since $ BD $ bisects $ \angle ABC $, it divides $ \angle ABC $ into two congruent angles ($ \angle ABD $ and $ \angle CBD $).
## Step1: Recall the definition of an angle bisector
An angle bisector is a line (or segment) that divides an angle into two congruent angles.
## Step2: Apply the definition to $ BD $ and $ \angle ABC $
Since $ BD $ is the angle bisector of $ \angle ABC $, it divides $ \angle ABC $ into 2 congruent angles.
# Answer:
it divides the angle into 2 congruent angles

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QUESTION IMAGE

Question

Explanation:

Part a

Step1: Recall the definition of a rhombus

Step1: Apply the Reflexive Property

Step1: Identify the sides of the triangles

Step2: Apply the SSS congruence theorem

Answer:

Part b