a. how many different triangles are in $ \triangle mbc $?
b. if $ \triangle bry \cong \triangle crx $, then complete the
congruence statement.
$ \overline { r c } \cong $ $ \angle r y b \cong $
c. if $ \triangle b x m \cong \triangle c y m $, then complete the
congruence statement.
$ \overline { c y } \cong $ $ \overline { c m } \cong $ $ \angle m c y \cong $

Question

Accepted Answer

# Explanation:
## a. Counting Triangles
- **Step1: Identify Smallest Triangles**
    - Triangles like $ \triangle BRY$, $ \triangle CRX$, $ \triangle BRX$, $ \triangle CRY$
- **Step2: Identify Medium - sized Triangles**
    - Triangles like $ \triangle BXM$, $ \triangle CYM$, $ \triangle BRC$
- **Step3: Identify the Largest Triangle**
    - $ \triangle MBC$ itself

## b. Congruent Triangles ($ \triangle BRY\cong\triangle CRX$)
- **Step1: Corresponding Sides**
    - Since $ \triangle BRY\cong\triangle CRX$, by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), $ \overline{RC}\cong\overline{RB}$
- **Step2: Corresponding Angles**
    - $ \angle RYB\cong\angle RXC$

## c. Congruent Triangles ($ \triangle BXM\cong\triangle CYM$)
- **Step1: Corresponding Sides**
    - $ \overline{CY}\cong\overline{BX}$ (CPCTC)
    - $ \overline{CM}\cong\overline{BM}$ (CPCTC)
- **Step2: Corresponding Angles**
    - $ \angle MCY\cong\angle MBX$ (CPCTC)

# Answer:
a. $ 8$
b. $ \overline{RB}$, $ \angle RXC$
c. $ \overline{BX}$, $ \overline{BM}$, $ \angle MBX$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

a. Counting Triangles

b. Congruent Triangles (\( \triangle BRY\cong\triangle CRX\))

c. Congruent Triangles (\( \triangle BXM\cong\triangle CYM\))

Answer: