Question

given: rhombus tcbv,
(overline{cu}perpoverline{bv},overline{cs}perpoverline{tv})
prove: (overline{cu}congoverline{cs})

Explanation:

Step1: Definition of a rhombus

All sides of a rhombus are equal, so \( TV = BV \).

Step2: AAS (Angle - Angle - Side) Congruence

Since \( \angle CSU=\angle CUB = 90^{\circ}\), \( \angle T=\angle B \) (opposite angles of a rhombus are equal) and \( TV = BV \), by AAS congruence criterion \( \triangle CTS\cong\triangle CBU \).

Step3: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

If \( \triangle CTS\cong\triangle CBU \), then \( CU = CS \) (corresponding parts of congruent triangles).

Answer:

1. \( TV = BV \)
2. \( \angle T=\angle B \), \( \angle CSU=\angle CUB = 90^{\circ}\)
3. AAS (Angle - Angle - Side) Congruence