Question

Drag a statement or reason to each box to complete this proof. Given: segment mn is congruent to segment nl. Segment nl is congruent to segment jn. Segment jn is congruent to segment nk. Prove: triangle mnk is an isosceles triangle. Art: triangle nmk with horizontal base mk is drawn. Side kn of the triangle is extended to a point labeled as j. Side mn of the triangle is extended to a point labeled as l. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Statements Reasons 1. mn is congruent to nl Given 2. nl is congruent to jn Given 3. mn is congruent to jn Response area 4. Response area Given 5. Response area Transitive property of congruence 6. Triangle mnk is an isosceles triangle. Response area mn is congruent to nk jn is congruent to nk Definition of isosceles triangle Transitive property of congruence

Answer 1

To prove that triangle MNK is an isosceles triangle, we use the given congruences of segments and apply the transitive property to establish that two sides of the triangle are congruent, thereby fitting the definition of an isosceles triangle.

Step-by-step explanation:

To complete the proof that triangle MNK is an isosceles triangle, follow these steps with the given statements and reasons:

Segment MN is congruent to segment NL - Given

Segment NL is congruent to segment JN - Given

Segment MN is congruent to segment JN - Transitive property of congruence (from steps 1 and 2)

Segment JN is congruent to segment NK - Given

Thus, segment MN is congruent to segment NK - Transitive property of congruence (from steps 3 and 4)

Finally, by the definition of an isosceles triangle (a triangle having at least two congruent sides), we conclude that triangle MNK is an isosceles triangle because MN is congruent to NK.