Answer:
The pair of triangles that are congruent by the ASA criterion isΔ ABC and Δ XYZ.
The pair of triangles that are congruent by the SAS criterion is Δ BAC and ΔRQP.
Step-by-step explanation:
Two triangles are congruent by ASA property if any two angles and their included side are equal in both triangles .In triangles Δ ABC and Δ XYZ the equal side 5 is between the two equal angles. So these triangles are congruent by ASA criterion.
Two triangles are congruent by SAS if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle .In triangles Δ BAC and ΔRQP. the included angles A and Q are equal and hence the triangles are congruent by SAS criterion.
Answer:
The probability that Katie will draw a face card on her next turn is 3/13, or approximately 23%.
Step-by-step explanation:
In a regular deck, there are four suits (clubs, spades, hearts and diamonds). Each suit has 13 cards that go from 2 - 10 plus the Ace, King, Queen and Jack. Since Katie is playing using a 26-card deck of only two suits, then there are only two kings, two queens and two jacks in the entire deck. In order to find probability, we form a fraction where the denominator is the total number of outcomes, in this case 26, and the numerator is the number of desired outcomes, in this case the total number of face cards in the deck - 6. So, the probability that Katie will choose a face card on the next turn is 6/26, which simplifies to 3/13 in lowest terms.
Answer:
Height of the triangular face of the box is 12 cm.
Step-by-step explanation:
This question is not complete; please find the question as the attachment.
Volume of a triangular prism = Area of the triangular base × height
It's given in the question, Volume of the prism = 3240 cm³
Height of the prism = 30 cm
By substituting these values in the formula,
3240 = B × 30
B = 
B = 108 cm²
Area of the triangular face (B) = 
108 = 
108 = 9h
h = 12 cm
Therefore, height of the triangular face of the prism is 12 cm.
Answer:
5.2cm
Step-by-step explanation:
Rx = 30...divide both sides by r
x = 30/r <==
