Question

in 17 - 20, name the postulate that allows you to conclude that the triangles are congruent. (g6b)

1. △abc ≅ △dcb

18.
17.______
a) hl b) asa c) aas
a) sss b) sas c) hl
19.
20.
19.______
20.______
a) asa b) sas c) aas
a) sss b) sas c) hl
21)
given triangle nml is congruent to triangle rts, find the value of x?
21______
type the value on your screen in eduphoria.

Explanation:

Step1: Analyze 17

• For right - angled triangles \(\triangle ABC\) and \(\triangle DCB\):
• Hypotenuse \(AC = DB\) (marked as equal) and leg \(BC=CB\) (common side).
• By the Hypotenuse - Leg (HL) postulate, \(\triangle ABC\cong\triangle DCB\).

Step2: Analyze 18

• For the two right - angled triangles:
• Hypotenuse and one leg are marked as equal.
• By the Hypotenuse - Leg (HL) postulate, the triangles are congruent.

Step3: Analyze 19

• For the two triangles:
• Two sides and the included angle (vertical angles are equal) are marked as equal.
• By the Side - Angle - Side (SAS) postulate, the triangles are congruent.

Step4: Analyze 20

• For the two triangles:
• All three sides are marked as equal.
• By the Side - Side - Side (SSS) postulate, the triangles are congruent.

Step5: Analyze 21

• In \(\triangle NML\), using the angle - sum property of a triangle (\(\angle N+\angle M+\angle L = 180^{\circ}\)):
• \(\angle M=180^{\circ}-(55^{\circ}+65^{\circ}) = 60^{\circ}\).
• Since \(\triangle NML\cong\triangle RTS\), \(\angle R=\angle M = 60^{\circ}\).
• Set up the equation \(2x + 30=60\).
• Subtract 30 from both sides: \(2x=60 - 30\).
• \(2x = 30\).
• Divide both sides by 2: \(x=\frac{30}{2}=10\).

Answer:

1. A. HL
2. C. HL
3. B. SAS
4. A. SSS
5. \(x = 10\)