Question

1. write three valid congruency statements given the triangles below.

directions: given the congruency statement, list all congruent angles and sides.

1. △abe≅△mnp

write another valid congruency statement:

1. △qry≅△jls

write another valid congruency statement:

1. given △stu≅△klm, complete each of the following statements.
2. given △bcm≅△zyr, find each missing measure.
3. given △acp≅△lnx, find each missing measure.

Explanation:

Step1: Identify congruent parts for first question

Corresponding vertices give congruency statements.
a) $\triangle TPW\cong\triangle DGH$
b) $\triangle TWP\cong\triangle DHG$
c) $\triangle PWT\cong\triangle GHD$

Step2: For $\triangle ABE\cong\triangle MNP$

Angles: $\angle A\cong\angle M$, $\angle B\cong\angle N$, $\angle E\cong\angle P$
Sides: $\overline{AB}\cong\overline{MN}$, $\overline{BE}\cong\overline{NP}$, $\overline{AE}\cong\overline{MP}$
Another congruency statement: $\triangle EAB\cong\triangle PMN$

Step3: For $\triangle QRY\cong\triangle JLS$

Angles: $\angle Q\cong\angle J$, $\angle R\cong\angle L$, $\angle Y\cong\angle S$
Sides: $\overline{QR}\cong\overline{JL}$, $\overline{RY}\cong\overline{LS}$, $\overline{QY}\cong\overline{JS}$
Another congruency statement: $\triangle YQR\cong\triangle SJL$

Step4: For $\triangle STU\cong\triangle KLM$

a) $\overline{TU}\cong\overline{LM}$
b) $\overline{KM}\cong\overline{SU}$
c) $\overline{LK}\cong\overline{TS}$
d) $\angle M\cong\angle U$
e) $\angle T\cong\angle K$
f) $\angle UST\cong\angle MKL$
g) $\triangle UST\cong\triangle MKL$
h) $\triangle TUS\cong\triangle KLM$

Step5: For $\triangle BCM\cong\triangle ZYR$

a) $CM = YR=11$ m
b) $BM = ZR$ (not given), assume no - additional info so no value
c) $YZ = BC = 8$ m
d) $m\angle B=m\angle Z$ (not given), assume no - additional info so no value
e) $m\angle M = m\angle R=45^{\circ}$
f) $m\angle Y=m\angle C = 103^{\circ}$

Step6: For $\triangle ACP\cong\triangle LNX$

a) $XL = AP = 13$ cm
b) $AC = LN$ (not given), assume no - additional info so no value
c) $PC = NX = 21$ cm
d) $m\angle L=m\angle A = 29^{\circ}$
e) $m\angle C=m\angle N$ (not given), assume no - additional info so no value
f) $m\angle X=m\angle P$ (not given), assume no - additional info so no value

Answer:

1.
a) $\triangle TPW\cong\triangle DGH$
b) $\triangle TWP\cong\triangle DHG$
c) $\triangle PWT\cong\triangle GHD$
2.
Angles: $\angle A\cong\angle M$, $\angle B\cong\angle N$, $\angle E\cong\angle P$
Sides: $\overline{AB}\cong\overline{MN}$, $\overline{BE}\cong\overline{NP}$, $\overline{AE}\cong\overline{MP}$
Another congruency statement: $\triangle EAB\cong\triangle PMN$
3.
Angles: $\angle Q\cong\angle J$, $\angle R\cong\angle L$, $\angle Y\cong\angle S$
Sides: $\overline{QR}\cong\overline{JL}$, $\overline{RY}\cong\overline{LS}$, $\overline{QY}\cong\overline{JS}$
Another congruency statement: $\triangle YQR\cong\triangle SJL$
4.
a) $\overline{LM}$
b) $\overline{SU}$
c) $\overline{TS}$
d) $\angle U$
e) $\angle K$
f) $\angle MKL$
g) $\triangle MKL$
h) $\triangle KLM$
5.
a) $11$ m
b) No value (not given)
c) $8$ m
d) No value (not given)
e) $45^{\circ}$
f) $103^{\circ}$
6.
a) $13$ cm
b) No value (not given)
c) $21$ cm
d) $29^{\circ}$
e) No value (not given)
f) No value (not given)