con and sim qns pls send help

[magic summit]

yall can someone help me with these

theres also more but im not sending all here yet

also pls use congruence and similarity only

[swift trellis]

so for problem 4, they give you two angles that are congruent, one from each triangle, and they give you the lengths of the two sides that are opposite of those two angles. then, you can form a ratio of those two side lengths.

so this is DB and AB, with lengths 8 and 12, and their ratio is 8/12 = 2/3.

so now, for part (a), you want to find AC. side AC is opposite of angle ABC. angle DBE and angle ABC are opposite angles, so they are congruent. this means that the side DE, which is opposite of DBE, can form a ratio with side AC, and this ratio will have to equal the ratio you found earlier. so you can set 2/3 = 12/AC and solve for AC.

(and notice that I set 2/3 = 12/AC instead of 2/3=AC/12. this is because in the original ratio, the numerator came from triangle DBE so the other ratio should do the same. just want to point out a common mistake)

all this is saying is that, triangle DBE is 2/3rds the size of triangle ABC, and any side from DBE is 2/3 of the matching side from ABC. you just have to know which sides are matching (which are the sides that are opposite of angles that are congruent)

for problem 5, I guess you have to assume that the diagram is to scale and angle PQR is congruent to angle ABC. I don't really see a way around this. anyway, the sides opposite from those angles are sides PR and AC, with lengths 8 and 4 respectively. their ratio is 8/4 = 2, so basically, triangle PQR is 2x the size of triangle ABC.

for part (b), side PQ matches with side AB, and we know that it is twice the size. so you can make the equation (x+5)=2*x, and this gives you that x=5. so when you plug x back into x+5, you get that side PQ is 10.

I hope you with these you can figure out 4b and 5a by yourself! let me know if you have any more questions!