Answer:
PO = 11, LQ = 4, NQ = 12, perimeter of NLP = 24
Step-by-step explanation:
The centroid is the point where the medians intersect each other.
A median divides the side it intersects in 2 equal parts.
So, if NP = 11, then PO = 11
The medians of a triangle intersect each other in the ratio 2:1
So, if NL = 8, then LQ = 4 and NQ = 8+4 = 12
if ML = 10, LP = 5
Finally, the perimeter of the triangle NLP is
NL + NP + LP = 8 + 11 + 5 = 24
Answer:
The interior of the triangle are congruent as they are equal in size at point at point l, k, m proof is the line of symmetry shows a 4 way rotation.
We know from how the line represents 2 triangles that equally make an equal sided square should we draw lines
For the g, h, i, j to show a 4 way rotation- should we draw 2 more triangles.
The second shape has congruent angles as the rotation is 2 and angles shown indicate the symmetrical value as midway point are the same also. So while all 3 sets of the second angles are congruent if we make a square shape 8/8 angles have the same degree as one another as there will be 4 triangles in shape 1 and shape 2.
Whilst the rotation is less, this is simply as the base is on the outside and sides are the same- creating a wider perimeter as it enlarges the shape. this may confuse but to prove again we can compare a rotation to equal curve triangles folded within a regular circle shape or just like the first example create 4 triangles and draw 2 lines of symmetry. just like folding a regular square. For full flip rotation within a shape we have found side length is not equal but angles must be 3 of the same for 2 way rotation within a larger shape and 3 equal angles with longer length for rotation within its first found square shape.
Step-by-step explanation:
Answer:
Both are congruent
Step-by-step explanation:
7. SSS congruence
KN=KM ........Side
KI=MI ........Side
LN is a common side
Thus by SSS congruence both triangles are congruent
8. ASA congruence
angles PRO=TRS ..........vertically opposite angles are equal
angles POR=RTS ..........given to be equal in the question
angle OPR=180-PRO-POR ...angle sum property of triangle
angle RST=180-RTS-TRS ......angle sum property of triangle
so OPR=RST as PRO=TRS and POR=RTS
line PO=TS .......given in question
so
OPR=RTS ...........angle
line PO=TS .........side
POR=RTS ...........angle
Thus by ASA congruence both triangles are congruent